Mix the Thai green curry paste, coconut milk, lime zest and juice, garlic, ginger, fish sauce, and sesame oil in a large bowl. Add the chicken drumsticks and toss so the chicken is fully coated.
Place the chicken in a large ziplock bag and refrigerate for at least 2 hours.
Take the chicken from the refrigerator and spread the drumsticks out evenly on a baking sheet. Sprinkle with sesame seeds and bake at 350 degrees for 30 minutes. Remove from oven and brush each chicken drumstick with the melted ghee, then bake for 30 more minutes.
Serve with lime wedges and a sprinkling of sesame seeds and cilantro.