In a large bowl, whisk together the soy sauce, sherry, and white sugar until the sugar is dissolved. Add the drumsticks, and toss to coat. Cover the bowl with a lid (or plastic wrap) and marinate the chicken for at least four hours, but preferably overnight.
Heat the grill to 350º F and brush the grates with oil. Remove the chicken from the marinade and sprinkle with plenty of black pepper (discard remaining marinade). Place the drumsticks on the grill. Cook, turning once or twice until the skin is lightly charred and the chicken is cooked through, about 30-35 minutes. Remove the drumsticks from the grill and let them rest for about 5 minutes. Serve.
Preheat the oven to 400º F. Remove the chicken from the marinade and sprinkle with plenty of black pepper (discard remaining marinade). Heat the oil in a large pan over medium-high heat. When the oil starts to shimmer, add the drumsticks to the pan, cooking in batches if necessary. Sear the chicken on all sides until the skin is lightly browned. Transfer the drumsticks to a baking dish and place it in the oven. Bake until the chicken is cooked through, about 20-25 minutes. Let the drumsticks rest for about 5 minutes. Serve.