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WEST HOLLYWOOD, Calif. — Martha Stewart arrived for dinner at the back-room chef’s table of the Nice Guy restaurant here recently, on what happened to be Taco Tuesday. The specialty of the house, the waitress told her, was its own interpretation of a Jack in the Box taco, a staple of Southern California drive-through fast-food cuisine.

She had just come from a party given by a friend, the White House decorator Michael S. Smith, for a book entitled “Great Houses, Modern Aristocrats.” But the unflappable doyenne of cooking, craftmaking, décor and home entertaining, used to striding between worlds, didn’t blink. She ordered two.

In blew the rapper Snoop Dogg, her friend and soon-to-be TV co-host, and sat down. Ms. Stewart offered him one.

“What did they call this?” she said. “A Jack in the Box taco?”

“Oh, come on, no you didn’t,” Snoop Dogg said. “I know what this is. I’ve been getting these at 2 in the morning.”

She ordered sauvignon blanc; he ordered a Coke. Dinner had begun.

Ms. Stewart, 75, and Snoop Dogg, 45, despite their differences, are regular dining companions, a fact that may or may not surprise you. VH1, the cable network, is rather hoping that it does — and that that surprise will be a potent draw for its new series, “Martha & Snoop’s Potluck Dinner Party,” whose premiere is Monday night.

“If you would’ve told me five years ago these two would have had a TV show I would’ve laughed myself sick,” said SallyAnn Salsano, an executive producer of the show. But that is the desired effect of “Martha & Snoop’s Potluck Dinner Party,” which plays the opposite public personas of its hosts — she, the often-parodied picture of Westport perfectionism, he the stoner-pimp of Long Beach — for maximum effect: She says potato, he says potizzle.

(Their private personas may be more similar than they let on: They are, after all, both wealthy celebrities of decadeslong standing. When Snoop Dogg arrived at dinner wearing a shirt, sweater vest and bow tie by Polo Ralph Lauren, Ms. Stewart chuckled her approval. “You know, I live next door to Ralph, in Bedford,” she said. “I have the farmette next to his estate.”)

On the show, the two prepare meals in a his-and-hers set of adjoining kitchens — his, purple and gold; hers, shelter-magazine white — with a revolving cast of celebrity friends, then sit down to eat and banter.

Seth Rogen, Ice Cube, Wiz Khalifa, Rick Ross, the N.B.A. player Chris Bosh and the model Ashley Graham all filmed appearances. “This is the weirdest group of people ever on a stage together,” Mr. Rogen said on the show. (Despite the potluck title, the guests do not bring dishes of their own.)

“The world that we live in, everybody is going in each other’s kitchen nowadays,” Snoop Dogg said philosophically. “Before, certain people wouldn’t go into other people’s kitchens.”

He added: “One thing about food, it’s a great conversation piece. That’s what’s missing in a lot of the world, conversation.”

Conversation, of the viral video clip kind, is the calling card of “Martha & Snoop’s Dinner Party,” which is less stringent about cooking preparations (though all of its recipes will be available online) and more free-form schmoozing: “The View” as recast by “Martha Stewart Living” and “XXL” magazines.

Ms. Stewart’s orbit is already more varied than some may expect. At her last Thanksgiving, she hosted, among others, the photographer Terry Richardson, the Italian multimillionaire investor and art collector Johnny Pigozzi and the power publicist Peggy Siegal. But Snoop Dogg is bringing still newer friends into her orbit.

“I didn’t know half the people” who came on the show, she said. “I knew who Wiz Khalifa was, but I didn’t know him. I didn’t know Fredwreck” — the show’s D.J., announcer and all-purpose hype man — “and now he’s my best friend.”

She turned to Snoop Dogg, conspiratorially.

“Kevin, who works for me, has a big crush on Wiz Khalifa,” she said.

“Oh, for real?” he said.

“Oh, yeah, he just thinks he’s so attractive,” Ms. Stewart said. “He is a very cute kid.”

Snoop Dogg’s guests seemed to be more aware of Ms. Stewart.

“She’s the queen in hip-hop,” he said. “All the hip-hop people, when they all came on the show, they all were like, ‘Martha, pleasure to meet you, I love you.’”

The hosts, and their guests, swap techniques and terminology, and the education goes both ways. Ms. Stewart taught him about preparation and presentation; he slipped in his own more free-form methods. He brought on an uncle who sprinkled everything with a spice blend he referred to as “a little bit of Jesus.”

“‘A little bit of Jesus!’” Ms. Stewart said, laughing. “No one ever said that in my mother’s kitchen. My mother said, ‘This is parsley.’”

(Snoop Dogg coyly insinuated that he and his friends — Mr. Khalifa has his own branded strain of marijuana — also sprinkled in a bit of their own preferred herb from time to time, including during a cook-off challenge that pitted his chicken wings against Ms. Stewart’s fried chicken. “I don’t know anything about that,” Ms. Stewart said. “I don’t smoke.”)

This is only the most recent venture from Ms. Stewart and Snoop Dogg, who have a long, if sporadic, history of working side-by-side on television, reliably generating ratings, laughs and goggle-eyed coverage. In their first appearance together, on Ms. Stewart’s television show in 2008, they made mashed potatoes and had a vocabulary lesson. (Ms. Stewart had several rappers on her show, she said; the only one who ever declined was Eminem.)

In their most publicized event, they sat together on Comedy Central’s roast of Justin Bieber in 2015, in which Ms. Stewart broke character to work blue. She gave Mr. Bieber instructions on how to make a prison shank, poking fun at her own five-month incarceration, and encouraged him to find a “player in the boardroom and a freak in the bedroom” — and suggested herself.

“All my people were saying she had got, like, a secondhand high,” Snoop Dogg said. “She killed it. They couldn’t believe she was that good.”

It was a decisive shift away from the Martha Stewart with the carefully tended vegetable patch and the regular reservation at the Four Seasons. Certain people in her office were against the idea, and she admitted it was “an odd scenario for me to be in.”

“But it worked,” she said. “It brought me a credibility in a broad spectrum of our society that I hadn’t had before.”

She mimicked a new fan: “Oh, that’s Martha, she’s the lady who makes my sheets. She’s pretty cool!”

Chris McCarthy, the president of MTV, VH1 and Logo, who had been pondering a cooking program that would fit in with VH1’s millennial-facing, pop-culture-obsessed slate, was one who took notice.

“My friend said, ‘Have you seen this clip of the Bieber roast? Martha Stewart was on there with Snoop,’” he said. “I said, ‘That’s the show.’’’

“They are the modern odd couple,” Mr. McCarthy said. “They have different points of view and it’s not the ones you’d think for each character.”

That phrasing is telling. Ms. Stewart and Mr. Dogg are real-life people, but they are also billboard-size brands. Their footprints and their followings — @MarthaStewart on Twitter: 3.34 million; @SnoopDogg on Instagram; 13.1 million — are large.

And their awareness levels are sky-high, according to the Q Scores Company, which tracks such things: Ms. Stewart’s and Mr. Dogg’s are in the 70 percent range, more than double the average celebrity’s and roughly in line with LeBron James’s.

They represent a diversified portfolio of brand extensions, and sometimes themselves slip into brand-speak: “The Justin Bieber roast has brought a huge awareness of Martha all over the globe,” Ms. Stewart said.

Snoop Dogg has made marijuana a centerpiece of his business pursuits, like his cannabis-lifestyle media platform, Merry Jane; his line of cannabis products, Leafs by Snoop; and a venture capital fund, Casa Verde Capital, dedicated to investing in cannabis-related start-ups.

Merry Jane is producing both the “Martha & Snoop” show and a scripted series, “Mary + Jane” for MTV, and he also hosts a newscast called “GGN” on his own WestFestTV YouTube channel, and will soon co-star in James Franco’s thriller, “Future World.” His most recent studio album, “Coolaid,” is his 14th, and in October he was given the “I Am Hip Hop” Icon Award at the 2016 BET Hip Hop Awards.

Ms. Stewart is starting a line of Martha Stewart Cafes (the first in the Starrett-Lehigh Building in New York, where Martha Stewart Living Omnimedia is headquartered). She recently published her 87th book, has partnered with the meal kit label Marley Spoon, runs an online marketplace for American-made craft goods on Amazon.com and has licensed lines of furniture, cabinetry, countertops and ranges at Home Depot, home goods at Macy’s, and Martha-branded products are available at Staples, PetSmart and Michaels. (No coincidence, many of Ms. Stewart’s own products are used on “Martha & Snoop’s Potluck Dinner Party.”)

Asked how she thinks of herself and her brand, Ms. Stewart had one word: “Expansive.”

With all that on their shoulders, Snoop Dogg and Ms. Stewart have to keep innovating their messaging and expanding their audiences, not to mention their opportunities. (“I think there’s a lot of legs in a brand with the two of them together,” Mr. McCarthy said, envisioning “so many different products and extensions.”)

They have been on a press blitz to promote the show, arriving at dinner after a full day of interviews; they had taped an appearance on Ellen DeGeneres’s show that would be broadcast the next day, along with their interview on Ryan Seacrest’s radio show.

But the two prefer to speak of the show in terms of fun, not business.

“This is a departure but it makes sense to me,” said Ms. Stewart, tucking into a plate of Scottish salmon at the chef’s table. (Snoop Dogg chose pepperoni pizza.) “It’s right for the time, I think, when we do need a little bit of levity in our lives, because of what’s going on.”

She gave a little sigh. It was the evening of Game 1 of the World Series, and Snoop Dogg had requested the TV be put on so they could watch. (He supports the Dodgers; Ms. Stewart, the Yankees. “I have front row seats for the Yankees from my banker friends at Bank of America,” she said.) Between innings, a “Donald Trump for President” ad came on.

“Angry,” Ms. Stewart said. She and Snoop Dogg both support Hillary Clinton; he played a benefit concert in Philadelphia during the Democratic National Convention. (She remembered Mr. Trump as “extremely unkind, to me and my team,” when she starred on an ill-fated season of “The Apprentice: Martha Stewart” in 2005.)

Their show, as it happens, premieres Nov. 7, and they will compete over chicken the night before two other unlikely adversaries compete for the country.

“There’s going to be so much talk,” Ms. Stewart said. “Maybe they’ll go to us for comic relief.”