Make small slits into chicken; set aside. In a medium bowl, add all the marinade ingredients and whisk until well incorporated. Add drumsticks and toss until well coated. Cover and transfer to the refrigerator for 24 hours.
Preheat oven to 425ºF and lightly grease a baking sheet lined with foil. Place a rack on baking sheet and then drumsticks; reserve marinade. Lightly brush on where there are patches without marinade on. Transfer them to the preheated oven and cook for 20 minutes. Remove from heat, flip them over and brush on brushing marinade. Return to oven and bake for another 20 minutes or until the internal temperature reaches 165ºF. Once again remove from heat and brush on the remaining marinade. Turn oven to broil and cook chicken for 3 to 5 minutes or until start to darken. Remove again, flip them over and return to darken the other side.