Preheat a grill for cooking over medium heat. Whisk together the ginger, 2 tablespoons coconut milk, 1/4 cup fish sauce, 2 tablespoons honey, juice of 1 lime, half the minced garlic, 1 teaspoon salt and a few grinds of pepper in a large bowl. Pierce the skin of the drumsticks all over with the tip of a knife or fork. Toss the drumsticks with the marinade to coat and set aside.