Preheat oven to 425°F. Line a baking sheet with foil and place a wire rack on top. Lightly grease the rack with cooking spray.
Pat the chicken drumsticks completely dry with paper towels. Moisture is the enemy of crispy skin, so take your time here.
In a large bowl, combine the baking powder, cornstarch, salt, black pepper, garlic powder, onion powder, and smoked paprika. Add the drumsticks and toss until evenly coated. Drizzle in the olive oil and toss again so the coating lightly adheres.
Arrange the drumsticks in a single layer on the wire rack, making sure they are not touching so air can circulate. Sprinkle with the extra ½ teaspoon of baking powder if using.
Bake for 25 minutes, then flip the drumsticks. Bake for another 20 to 25 minutes until the skin is deep golden and crisp and the internal temperature reaches 175°F.
For extra crunch, broil for 2 to 3 minutes at the end while watching closely. Let rest 5 minutes before serving.