Use sharp kitchen scissors or a sharp knife to carefully cut the chicken along the bone. Use your hands to fan out each drumstick, flattening each slightly. Then put the drumsticks in a gallon size plastic bag.
Put the coconut milk, minced garlic, vegetable oil, oyster sauce, soy sauce, fish sauce, sugar, and fresh cilantro in a bowl. Whisk until evenly combined.
Pour this mixture into the bag with the chicken. Massage the bag and marinate in the fridge for several hours.
Preheat the grill or Blackstone griddle to medium heat. Remove chicken from marinade, season with kosher salt and pepper.
Cook the chicken 12 to 16 minutes total, flipping a few times. Brush with the extra marinade halfway through cooking. The chicken should have an internal temperature of 165 degrees.