He’s not going to like it if I write this, but Brooks Headley is a lot of people’s hero. For some of you, the hero worship might have started as far back as the early 1990s, when Headley played drums in Born Against, Universal Order of Armageddon, Skull Kontrol, or one of your other favorite hardcore bands. But the music world is not the only place he would have earned your admiration. Perhaps you became a devotee after eating at Del Posto, a high-end Italian restaurant in New York City, where he drew attention as the restaurant’s mischievous pastry chef. His were desserts in the expanded field—dolce, for Headley, included vegetables, as in his infamous dish involving chocolate and eggplant, or gelato paired with carrots. In a definitive way, he became everyone’s hero with the publication of his cookbook, Fancy Desserts, which collects his jaunty, punk-inspired recipes into a gastronomic portrait of the underground. Take, for example, popcorn with nutritional-yeast pudding, a dish whose origins include a punk house he shared with bandmate Mick Barr and the tasting menu at Coi, a Michelin two-star restaurant in San Francisco. Though Headley was already in possession of a James Beard Award at the time of its publication, the book nonetheless cemented his status in the food world at large.

Today, the reason you still keep a framed picture of Headley on your nightstand has to do with Superiority Burger, a monastic six-seat restaurant built around the humble veggie burger. The eponymous dish is a pretty simple concoction: the ingredients top out at chickpeas, walnuts, caramelized onions, fennel seeds, chili powder, cracked pepper, carrots, quinoa, olive oil, and potato starch. It is served on an industrially produced bun. But the straightforwardness is part of the trick. Since it opened, in 2015, Superiority Burger has earned a cult following, not only for the burger, but for a particular ethos ingrained in Headley’s vegetarian cuisine. You find it in his menu’s inquisitive and reverent attitude toward ingredients—during the 2019 holiday season, the restaurant celebrated the arrival of a festive, ruby-colored winter-greens salad, imploring on its Instagram, “almost xmas? eat salad!” Indeed, it’s this idiosyncratic, almost self-deprecating sense of humor that keeps the place from being dogmatic.

After our conversation, which focused primarily on the burger, Headley became my hero too. Accessibility, both in terms of taste and price, is no small feat in New York City, a place where success often depends on your ability to distinguish yourself from others. But herein lies the humble virtue (and eccentric humor) of his approach to food. To borrow the slogan of Reese’s Peanut Butter Cups: there is no wrong way to eat a...