Combine the lemon rind, lemon juice, olive oil, 1/4 cup chopped mint, ground cumin, salt, black pepper, and minced garlic in a large bowl. Add the chicken drumettes, and toss to coat. Cover the drumettes, and marinate in the refrigerator for 20 minutes, tossing occasionally.
Preheat the broiler. Place half the drumettes on a broiler pan coated with cooking spray, and broil for 15 minutes or until browned. Turn the drumettes over, and broil for 10 minutes on the other side or until the drumettes are done. Repeat the procedure with the remaining drumettes. Sprinkle drumettes with the remaining 1/4 cup chopped mint before serving (either hot or at room temperature).