NO ONE USED TO CARE what a chef wore outside the kitchen. From 2000 to 2010, Adam Rapoport was an editor at GQ and he doesn’t recall the magazine ever touting a chef as a fashion icon during his tenure. “There was nothing alternative about the food world,” said Mr. Rapoport, now editor-in-chief at Bon Appetit magazine. “You were working. You were manual labor in the kitchen.” Back then, traditional chefs like Daniel Boulud and Jean Georges ruled the culinary world. They were known for their precise tasting menus and scrupulously appointed dining rooms, not their style. Mr. Boulud was never photographed in a houndstooth...