01 - Set grill to medium heat, targeting approximately 350°F. Allow grates to fully heat for even cooking.
02 - In a large bowl, combine olive oil, smoked paprika, garlic powder, onion powder, salt, and black pepper. Mix until a smooth paste forms.
03 - Add chicken thighs and drumsticks to the bowl, tossing to coat every piece thoroughly in the seasoning mixture. Ensure the rub covers both the skin and underside of each piece.
04 - Place chicken on the grill skin-side down. Cover and cook for 5 to 7 minutes until the skin turns golden brown and develops a crisp texture.
05 - Flip each piece and generously brush the top with barbecue sauce. Grill for an additional 6 to 7 minutes.
06 - Turn and baste the chicken with barbecue sauce every 5 minutes. Continue grilling for 20 to 25 minutes total until the internal temperature reaches 165°F and the sauce has caramelized into a sticky glaze.
07 - Transfer chicken off the grill and let it rest for 5 minutes to allow juices to redistribute before serving.