Blend garlic, oregano, paprika, salt, jalapeno, scallion, cilantro, lime juice, and olive oil in a food processor.
Pour marinade over drumsticks and toss. Add black pepper. Refrigerate 4 hours or overnight.
Preheat oven to 375°F. Place chicken on a baking rack. Bake about 1 hour.
Make BBQ sauce: in a nonstick pan combine ketchup, vinegar, soy sauce, and honey. Cook on low about 1 minute.
At 55 minutes, remove chicken and brush with BBQ sauce.
Set oven to broil. Broil 3-5 minutes until sauce is thick and caramelized.
Garnish with cilantro. Serve.