Pat the chicken drumsticks dry with paper towels and let them rest at room temperature for 20 minutes.
Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper or foil.
In a small bowl, mix garlic powder, onion powder, paprika, salt, and black pepper.
Rub the seasoning evenly over all sides of the drumsticks.
Arrange the drumsticks on the baking sheet or on a rack set over the sheet, spacing them apart.
Bake for 20 minutes, then flip the drumsticks and continue baking for another 20 minutes.
While the chicken bakes, combine ketchup, honey, brown sugar, soy sauce, and BBQ sauce in a small saucepan.
Simmer the sauce over medium-low heat, stirring often, until thick and glossy, about 5 minutes.
Remove the chicken from the oven and brush generously with BBQ sauce on both sides.
Return the chicken to the oven and bake for 5 more minutes, or broil briefly until caramelized.
Remove from the oven when internal temperature reaches 165°F (74°C) and let rest for a few minutes before serving.