Season drumsticks with salt and pepper. Roast drumsticks for 15 minutes.
Whisk together the soy sauce, honey, and olive oil. Brush drumsticks with glaze at halfway point (make sure to separate half glaze for raw application, the rest will be for tossing before serving).
Continue cooking drumsticks for 15 more minutes, until cooked all the way through.
Toss drumsticks with the rest of the glaze and sprinkle with sesame seeds.