Preheat the oven to 425°F (220°C). Line a baking sheet with aluminum foil and place a wire rack on top if you have one.
Heat 1 teaspoon olive oil in a small saucepan over medium heat. Add the diced onion and minced garlic and cook, stirring, until softened, about 2–3 minutes.
Add 1/2 cup honey and 2 tablespoons soy sauce to the saucepan and stir to combine.
Whisk 1/4 cup chicken broth with 1 teaspoon cornstarch until smooth, then pour into the saucepan. Bring the mixture to a boil and cook, stirring, until the sauce thickens, about 5 minutes. Remove from heat and set aside.
Pat the 2.5 lb chicken drumsticks dry with paper towels. Season all sides with salt, black pepper, and 1/4 teaspoon crushed red pepper flakes.
Arrange the drumsticks on the prepared rack and bake for 10 minutes. Flip the drumsticks and bake another 10 minutes.
Brush the drumsticks with some of the honey-garlic sauce and bake for 5 minutes. Flip, brush the other side with sauce, then continue baking until the internal temperature reaches 180–190°F (82–88°C) and juices run clear, about an additional 5–10 minutes.
Remove the drumsticks from the oven, transfer to a serving plate, and pour any remaining sauce over them before serving.