In a food processor, blend the green curry paste, ginger, cilantro, salt, cayenne pepper, yogurt, and oil and process until smooth. Pour the marinade into a large glass bowl and add the drumsticks; toss to coat well. Cover the bowl and place it in the refrigerator for 3 hours, or overnight.
Preheat the oven to 450°F (230°C), line a large baking sheet with foil and place a well-oiled wire rack in the pan. Place the marinated drumsticks on the prepared rack and place the pan in the oven for 45 minutes, flipping the drumsticks halfway through. At the end of the cook time, switch the oven to broil and cook for an additional 3 to 5 minutes, or until the drumsticks appear crispy. Remove the pan from the oven and allow the drumsticks to cool slightly before serving. The drumsticks can be stored, covered, in the refrigerator for up to 3 days.
Substitutions: To make this recipe dairy-free or Paleo, use unsweetened dairy-free yogurt. To make this recipe vegetarian, use paneer or tofu instead of chicken