How to Make It
Whisk together olive oil, honey, salt, pepper, paprika, and cayenne in a medium bowl. Whisk in beer, garlic, and ginger.
Place drumsticks, olive oil mixture, and onions in a large zip top bag. Massage marinade into chicken. Let marinate in the refrigerator 6 hours or up to 24 hours.
Preheat a gas grill to medium (350°F to 400°F) on one side, or push hot coals to 1 side of a charcoal grill.
Remove drumsticks from marinade with tongs and place drumsticks on oiled grates over lit side of the grill. Discard onions and marinade. Grill drumsticks, covered, until skin is well marked and crispy, 5 to 6 minutes. Turn drumsticks over, and transfer to unlit side of grill. Grill, covered, until a thermometer registers 165°F when inserted into thickest part of a drumstick, 20 to 22 minutes, turning halfway through grilling. Remove from grill, and let rest 5 to 10 minutes before serving.