Combine the balsamic, honey, brown sugar, soy sauce, rosemary sprigs, and garlic cloves, in a large, re-sealable plastic bag. Shake and squeeze the contents of the bag to dissolve the honey and the brown sugar. Add the chicken drumsticks to the bag and seal with as little air as possible in the bag. Place in the refrigerator and marinate for 2 hours.
Preheat the oven to 450 degrees F.
Place the chicken drumsticks on a foil-lined baking sheet. Bake until the skin is caramelized and very dark in spots, about 30 to 35 minutes.
Meanwhile, place the marinade in a small saucepan. Bring the marinade to a boil (in order to kill bacteria). Reduce the heat to simmer and cook over low heat until thick, about 15 minutes. Reserve.
Use a pastry brush to brush some of the cooked marinade on the cooked chicken. Place the chicken on a serving platter. Sprinkle with the sesame seeds and the chopped parsley.
Cook's note: I like the rosemary and garlic flavors in the background. Brushing the cooked drumettes with the reduced marinade helps the flavors along. Also, re-moistening helps the parsley and the seeds to adhere.