Make a barbecue rub for the chicken: In a small bowl, combine brown sugar, paprika, 1 Tbsp salt, black pepper, chili powder, garlic powder and onion powder. Mix thoroughly.
Season chicken with 1/4 cup barbecue rub; reserve rest of rub for future use. Set chicken on racked sheet pan and bake uncovered 75–80 minutes, or to an internal temperature of 165ºF. Remove cooked chicken from oven and cut into quarters.
Bring a large pot of water to boil. Add corn; cook 10 minutes. Remove corn from water, cut into quarters and add smoked paprika, Cotija cheese, cilantro and 1-1/2 tsp salt.