Begin by patting the chicken drumsticks dry with paper towels. Season generously with salt, pepper, and crushed red pepper flakes.
In a large mixing bowl, combine honey, soy sauce, chicken broth, diced onion, minced garlic, and a pinch of salt. Mix well.
Add the seasoned chicken drumsticks to the marinade. Toss to coat evenly. Let them marinate for at least 30 minutes, or up to 4 hours for better flavor.
In a skillet or Dutch oven, heat olive oil over medium-high heat. Once hot, add the marinated drumsticks, reserving the marinade. Sear for about 5-7 minutes on each side until golden brown.
Pour the reserved marinade over the chicken. Bring to a gentle boil, then reduce heat to low. Cover and let simmer for about 30 minutes, or until cooked through.
In a small bowl, mix cornstarch with a tablespoon of water to create a slurry. Stir into the skillet after the chicken is cooked. Cook for an additional 5 minutes until the sauce thickens.
Remove from heat and transfer the drumsticks to a serving platter. Drizzle with the thickened sauce and serve hot.