Begin by preheating your oven to 425°F. Line a baking sheet with aluminum foil for easy clean-up, and if available, place a wire rack on top.
In a small saucepan, heat the olive oil over medium heat. Once the oil is hot, add the minced garlic and diced onions. Sauté them, stirring frequently, until fragrant and slightly softened.
Next, add the honey and soy sauce to the pan. In a separate bowl, whisk together the chicken broth and cornstarch until smooth. Pour this mixture into the pan and bring it to a boil. Allow the sauce to cook, stirring occasionally, until it thickens, approximately 5 minutes. Once done, remove the saucepan from the heat.
Pat the chicken drumsticks dry with paper towels to ensure a crispy finish. Arrange the drumsticks on the prepared rack, then season generously with salt, pepper, and crushed red pepper flakes.
Place the chicken in the preheated oven and roast for 10 minutes. After the initial 10 minutes, flip the drumsticks and continue cooking for another 10 minutes. Brush the chicken with some of the prepared sauce, then return to the oven for an additional 5 minutes. Flip the drumsticks one last time, coating the other side with sauce, and cook for another 5-10 minutes. The chicken should reach an internal temperature of 180-190°F, and the juices should run clear.
Serve the drumsticks hot, accompanied by rice and steamed vegetables if desired. Don’t forget to drizzle any remaining sauce over the chicken for added flavor!