In 2022, Sylvain Berneron, an industrial designer by training, began sketching a gold watch with an unusual asymmetric silhouette — a bit like a circle that had been put through a wringer. After showing the sketch to a handful of potential suppliers, he named it the Mirage, because the piece seemed so unlikely to get made.

“The only way I could make it happen was to pay 100 percent of my order in advance — 750,000 Swiss francs with zero clients,” Mr. Berneron said by phone last month from the Swiss city of Neuchâtel, where he lives and where his brand, Berneron, has its headquarters.

Generally known as a shaped watch, an industry category describing any timepiece that is not round, the Mirage takes its cues from the design of its hand-wound mechanical movement, visible through the case back.

“I was taught that good design is form following function,” Mr. Berneron said. “That’s why I designed a movement that would not be restricted. I let the wheels take the space they needed and once I had the gear train, I decided to go around the gears and drew the case shape around the movement.”

Before Mr. Berneron introduced the 38-millimeter model last year, he hoped he could sell 12 pieces, each at 55,000 Swiss francs ($64,980). The watch, now 61,000 francs, has since sold many multiples of that figure. “We are facing 100 times the demand of what I am able to produce,” he said. “We are currently sold out until 2029.”