Mix up all the chicken marinade ingredients, from rice wine vinegar to salt and pepper, in a large zip-top bag. Add the chicken drumsticks to the bag with the marinade. Refrigerate for at least 2-3 hours, up to overnight.
Preheat the oven to 425°F.
Toss the broccoli and cauliflower florets with avocado oil, sesame oil, and minced garlic. Season to taste with salt and pepper.
Create a boat of aluminum foil large enough to hold the chicken, and set it on the baking sheet to serve as a divider. Spread the vegetables out on the outside of the divider.
Roast at 425°F for 10 minutes.
Turn the vegetables, and add the marinated chicken to the aluminum foil tray, reserving the marinade for the next step. Roast the chicken and vegetables together for 15-20 minutes.
While the chicken and veggies are roasting, reduce the marinade on the stove to make a glaze. Make sure that it comes to a full rolling boil to kill off any bacteria.
When the broccoli and cauliflower are cooked, remove them from the pan and garnish with toasted sesame seeds.
Brush the drumsticks with the glaze, then broil for 3-5 minutes on each side. Garnish with toasted sesame seeds and chopped cilantro, if desired. Serve with roasted broccoli and cauliflower.
Notes
Don't worry about using the marinade as a glaze! We've taken lots of precautions to make sure it's safe to eat. The meat is refrigerated at all times, then you rapidly boil the marinade afterward. This helps thicken the sauce and cooks out any bad bugs that might have made it in, making it safe to use.