Preheat oven to 400°F (200°C). Line a baking sheet with aluminum foil for easy cleanup.
In a large bowl, combine olive oil, salt, black pepper, paprika, garlic powder, onion powder, and cayenne pepper. Add drumsticks and toss until evenly coated with the spice mixture.
Arrange drumsticks on the prepared baking sheet in a single layer, guaranteeing they don't touch.
Bake for 20 minutes, then remove and brush with BBQ sauce. Return to oven and bake for 7-8 minutes.
Flip drumsticks, brush with more BBQ sauce, and bake for another 7-8 minutes.
Turn oven to broil setting. Broil drumsticks for 3-4 minutes per side, brushing with additional sauce until juices run clear and internal temperature reaches 165°F (74°C).