Preheat the oven to 450 degrees F. Set a wire rack on a rimmed baking sheet. Put the drumsticks on the rack and season both sides generously with salt and pepper. Bake 30 minutes; flip the drumsticks and continue baking until golden and crisp, about 30 more minutes.
Meanwhile, make the sauce: Bring the apple juice, vinegar, soy sauce, honey, lemon zest, red pepper flakes and a pinch of salt to a high simmer in a large skillet over medium-high heat. Cook until the sauce is syrupy and coats the back of a spoon, 20 to 25 minutes. Set aside until the chicken is done.
Stir the sesame seeds into the sauce, if using, and warm over medium heat, if necessary. Transfer the chicken to a large bowl. Add the sauce and butter and toss to coat. Season with salt and pepper. Transfer the chicken to a platter and drizzle with any remaining sauce from the bowl.