In a large pot, combine all the brine ingredients except the ice and chicken. Bring the mixture to a boil, then remove it from the heat.
½ cup (72 g)* kosher salt, ½ cup (100 g) granulated sugar, 8 whole garlic cloves, 2 cups (200 g) fresh ginger, roughly chopped, 5 whole star anise, 6 cups (1.42 liters) water
Immediately add the ice to the hot brine and stir until it’s fully melted and the brine is cooled below 40°F (4°C).
8 cups (1.9 liters) ice cubes
Rinse the drumsticks under cold water, then add them to the cooled brine. Cover and refrigerate for 3 to 4 hours.
4-5 lbs. (1.8-2.3 kg) chicken drumsticks
While the chicken finishes brining, make the marinade. In a large Ziploc bag, combine the hoisin sauce, soy sauce, rice wine vinegar, water, and minced garlic. Seal the bag and press to mix everything together.
1¼ cups (295 ml) hoisin sauce, ¼ cup (60 ml) low-sodium soy sauce, ¼ cup (60 ml) rice wine vinegar, ¼ cup (60 ml) water, 3 cloves minced garlic
Remove the drumsticks from the brine and pat off any excess moisture. Add the chicken to the bag with the hoisin mixture. Seal the bag and turn it over several times to coat the drumsticks completely.
Let the chicken sit in the marinade for 2 hours at room temperature, turning the bag occasionally so everything stays evenly coated.
Preheat the oven to 400°F (200°C). Line a large rimmed baking sheet with aluminum foil and set a rack on top. Lightly spray the rack with cooking spray.
Remove the drumsticks from the marinade and place them on the prepared rack. Wipe off any large bits of garlic sticking to the chicken and return those to the marinade (they tend to burn in the oven).
Bake the chicken for 40 minutes, then flip each drumstick and bake for another 40 minutes, for a total of 80 minutes.
While the chicken bakes, pour the remaining marinade into a saucepan. Bring it to a boil, then reduce the heat and let it simmer for 30 minutes to thicken slightly into a glaze.
Once the chicken is done baking, remove it from the oven and brush both sides with the warm glaze. Serve hot.