In a food processor, combine the yogurt, garlic, parsley, cumin, paprika, salt, and pepper. Process until well combined and parsley is finely chopped.
Add the yogurt mixture and the drumsticks to a large ziploc bag. Rub the marinade around the chicken legs, making sure to get it under the skin.
Marinade chicken for at least 30 minutes, up to 24 hours.
Preheat oven to 425 degrees F (218 degrees C). Arrange drumsticks on a lightly greased baking sheet. Bake for 25 minutes, then remove from oven and flip the chicken legs and bake for another 15 minutes, until cooked through and skin is golden brown. If necessary, broil the chicken for a few minutes to brown the skin.
Let chicken rest for five minutes before serving. Serve with feta cheese and naan, if desired.