In a large bowl or measuring cup, whisk together beer, olive oil, soy sauce, brown sugar, apple cider vinegar, minced garlic, paprika, ground cumin, dry mustard, crushed red pepper, black pepper, salt and lime juice until sugar and salt dissolve. Stir in chopped cilantro or parsley if using.

Prep chicken

Pat drumsticks dry with paper towels. Use a sharp knife to make two shallow 1/4-inch slashes through the thickest part of each drumstick (this helps flavor penetration and even cooking).

Marinate

Place drumsticks in a large zip-top bag or non-reactive container. Pour marinade over the drumsticks, pressing out excess air if using a bag and ensuring drumsticks are coated. Refrigerate at least 2 hours, preferably 6–8 hours. For best flavor, marinate up to 12 hours. Turn bag or stir drumsticks occasionally to redistribute marinade.

Grilling

Preheat grill

Remove drumsticks from refrigerator about 20–30 minutes before grilling to come closer to room temperature. Preheat a grill to medium heat (about 350–400°F / 175–200°C). Prepare a two-zone fire if using charcoal or set burners so there is a direct medium heat zone and an indirect zone.

Drain and season

Remove drumsticks from the marinade and let excess drip off. Discard used marinade. Lightly brush or rub each drumstick with a little olive oil if desired and season a small additional pinch of salt and pepper if needed.

Initial sear

Place drumsticks over direct medium heat and sear, turning every 2–3 minutes, until nicely browned on all sides (about 8–10 minutes). Watch for flare-ups and move pieces briefly to indirect heat if they char too quickly.

Finish over indirect heat

Move drumsticks to the indirect zone and close the lid. Grill until internal temperature reaches 175–180°F (79–82°C) measured at thickest part near the bone, about 15–25 more minutes depending on size. Turn once halfway through for even cooking. Total grill time typically 25–35 minutes.

Baste and glaze (optional)

During the last 5 minutes of grilling, brush drumsticks with the melted butter mixed with honey, turning and re-basting once to build a glossy finish. If honey is used, watch closely to avoid burning.

Rest

Transfer drumsticks to a clean platter, tent loosely with foil, and let rest 5 minutes to redistribute juices.

Finish & Serve

Sprinkle drumsticks with a small pinch of coarse sea salt to taste and a little chopped cilantro if desired. Serve hot with lime wedges and your choice of sides. Leftover drumsticks keep refrigerated up to 3 days; reheat gently in a 350°F oven until warmed through.