Prep the drumsticks: Pat the chicken dry with paper towels. Dry skin is key for crisping.
Toss with olive oil in a large bowl.
Mix the rub: In a small bowl, combine brown sugar, smoked paprika, garlic powder, onion powder, salt, pepper, and chili powder if using. Sprinkle over the chicken and toss to coat evenly.
Set up the grill or oven: Grill: Preheat to medium heat (about 375–400°F). Create two zones: one for indirect heat and one for direct heat.
Oven: Preheat to 400°F.
Line a baking sheet with foil and set a wire rack on top. Lightly oil the rack.
Start cooking: Grill: Place drumsticks on indirect heat, cover, and cook for 20–25 minutes, turning once.
Oven: Arrange drumsticks on the rack and bake for 25 minutes.
Make the glaze: Stir BBQ sauce with apple cider vinegar. This thins it slightly and adds tang that balances the sweetness.
Glaze and finish: Grill: Move drumsticks to direct heat.
Brush with sauce and cook 8–10 minutes, turning and glazing 2–3 times until charred in spots and sticky.
Oven: Brush with sauce and bake 10–15 more minutes, flipping and glazing once, until sticky and slightly caramelized. For extra char, broil 2–3 minutes at the end.
Check doneness: Use a thermometer. Internal temp should be 175–185°F at the thickest part (not touching bone). Dark meat is more tender above 175°F.
Rest and serve: Let the drumsticks rest 5 minutes.
Garnish with parsley, squeeze of lime if you like, and serve with extra sauce.