Place everything except the chicken in a 13-by-9-inch broiler-proof baking dish and whisk to combine. Lay the chicken in a single layer in the marinade and turn to coat. Cover, refrigerate, and marinate at least 12 hours and up to 24 hours, turning the chicken at least once during the marinating time. Remove the chicken from the refrigerator and let it sit at room temperature for about 30 minutes. Meanwhile, heat the oven to 475°F and arrange a rack in the middle. Turn all the chicken pieces skin-side up in the dish (if you’re using drumsticks, just turn to recoat them in the marinade). Bake until the chicken is starting to turn a dark brown color, about 40 minutes. Set the oven to broil and broil until the chicken skin is crisped, about 3 to 5 minutes more. Serve with the sauce on the side.