Preheat the oven to 400°F. Line a rimmed baking sheet with high-heat-resistant parchment paper and arrange the drumsticks on the baking sheet in a single layer.
Make the seasoning paste: In a medium bowl, mix the olive oil, kosher salt, black pepper, garlic powder, onion powder, smoked paprika, and cayenne pepper with a fork or a spatula.
Using a pastry brush or your hands, coat the chicken pieces with the seasoning paste.
Bake the drumsticks uncovered for about 40 minutes, until their internal temperature, measured with an instant-read thermometer and not touching a bone, reaches 165°F.
Baste the drumsticks with the pan juices using a clean pastry brush. Serve immediately.
Video
Notes
Check the drumsticks after the first 30 minutes. If they seem to be darkening too fast on top, loosely cover them with foil and keep cooking until they are cooked through.
Chicken should be fully cooked. It should reach an internal temperature of 165°F when measured with an instant-read thermometer, not touching the bone.
When I'm lazy, instead of making a seasoning mix, I arrange the drumsticks in the pan, spray them with olive oil, and sprinkle them with spices.
You can keep the leftovers in the fridge, in an airtight container, for 3-4 days. Reheat them in a 350°F oven to crisp the skin, or enjoy them cold! I sometimes remove the skin, cut them into chunks, and use them in a salad.