Poulet rôti—French for roast chicken —is a simple yet comforting affair of chicken, vegetables, and herbs. At Le Chêne in New York City, chef Alexia Duchêne puts her own spin on the dish, inspired by the many chickens she ate for Sunday suppers growing up. A whole chicken gets roasted atop carrots, potatoes, and onino, which become a side along with the built-in sauce from the pan drippings. Duchêne starts with a heritage bird, keeping the feet intact so they render into crisp nubs for diners to snack on. This recipe follows a similar process but is adapted for home cooks. It starts by coating the chicken in a flavorful compound butter that includes lemon zest, parsley, and piment d’Espelette —a variety of dried pepper with a fruity, slightly smoky flavor and mild heat. In the restaurant, this butter mixture includes garlic cloves that have been confited in olive oil until tender and jammy, but finely chopped or grated raw cloves make for a good substitute at home.…