Preheat the oven to 425°F (220°C). Line a baking sheet with aluminum foil and place a wire rack on top if available.
Heat 1 teaspoon olive oil in a small saucepan over medium heat. Add the diced onion and minced garlic and cook, stirring constantly, until softened and fragrant, about 2–3 minutes.
Add 1/2 cup honey and 2 tablespoons soy sauce to the saucepan. In a small bowl, whisk together 1/4 cup chicken broth and 1 teaspoon cornstarch until smooth, then pour into the pan.
Bring the sauce to a boil, then reduce heat and simmer until it thickens slightly, about 4–6 minutes. Remove from heat and set aside.
Pat the drumsticks dry with paper towels. Season all over with salt, black pepper, and 1/4 teaspoon crushed red pepper flakes.
Place the drumsticks on the prepared rack and roast in the preheated oven for 10 minutes. Flip the drumsticks and roast for another 10 minutes.
Brush or spoon some of the prepared sauce over the drumsticks, then return to the oven and roast 5 minutes. Flip the drumsticks, brush the other side with sauce, and roast an additional 5–10 minutes until internal temperature reaches 180–190°F and juices run clear.
Remove the drumsticks from the oven and let rest a few minutes. Serve with any remaining sauce spooned over the chicken.
