Preheat the oven to 450º F.
Place drumsticks on a rimmed baking sheet with a wire rack. Salt and pepper both sides of the drumsticks. Bake for 30 minutes. Flip the drumsticks and bake for an additional 30 minutes.
While baking the chicken, combine the apple juice, apple cider vinegar, soy sauce, honey, lemon juice, crushed red pepper and a pinch of salt. Simmer in a large skillet over medium-high heat stirring to create a syrup.
Combine the sesame seeds and melted butter. Add to the sauce.
Brush the sauce over the drumsticks and serve.