Prepare drumsticks by rinsing with water and patting dry with a paper towel. If desired, remove skin. Set aside.
In a large bowl, add balsamic vinegar, honey, sriracha, brown sugar, soy sauce, and garlic. Whisk together until smooth. Taste test sauce - if you'd like it spicy, add another tablespoon of sriracha. If you'd like it sweeter, add another tablespoon of honey.
Pour honey sriracha marinade in a large Ziploc bag. Add drumsticks and toss to coat. Squeeze excess air out of bag and seal. Let chicken marinate in the refrigerator for at least 2 hours, turning half way through if possible.
Preheat oven to 450 degrees F. Prepare a baking sheet by lining it with aluminum foil. Place an oven safe rack (sterling silver, not black coated) on top of the foil, so that the setup creates a makeshift grill.
Place drumsticks on rack setup and set bag with marinade to the side (do not throw away). Bake drumsticks in the oven for 30 minutes or until outside of chicken is caramelized and there are few dark spots.
While chicken cooks, pour marinade in a small saucepan. Bring to a boil over medium heat. Continue to heat marinade so that there are vigorous bubbles but sauce is not boiling over. Let sauce simmer for 10-15 minutes, stirring occasionally, until thickened. Sauce is ready once bubbles have become big & slow, sauce seems "spotted" (with bubbles), and the sauce can coat the back of a spoon. Set heat to low while chicken finishes.
When ready, remove chicken from oven. Using a baster brush, coat both sides of the dumbsticks with the thickened marinade. Return chicken to oven and cook for another 10 minutes.