Preheat gas or charcoal grill to roughly 350 F (medium-high on a gas grill). Meanwhile, season chicken with all-purpose seasoning and set aside, allowing it to reach room temperature before grilling. Once the grill is sufficiently hot, add the chicken skin-side-up and away from direct heat, then close the grill lid and open the vents. After about 15 minutes, flip the chicken and cover the grill again. After another 15 minutes, or so, remove chicken from the grill and place in a shallow pan. Pour about half of the barbecue sauce over the chicken, using a brush to coat each piece evenly. Use tongs to return the chicken to the grill and cook uncovered for an additional 10 minutes, or until the internal temperature reaches at least 170 degrees. Allow to rest for 5-10 more minutes. Serve with additional barbecue sauce on the side for dipping.