Pat the chicken drumsticks dry with paper towels; remove skin if desired for a less crispy result (skin left on yields crispier drumsticks).
In a large bowl, toss the drumsticks with 1 teaspoon baking powder until each piece is fully coated.
On a plate, combine 1/4 cup grated Parmesan, 1/2 teaspoon garlic powder, 1/2 teaspoon onion powder, 1/2 teaspoon chili powder, 1/4 teaspoon kosher salt, and 1/8 teaspoon ground black pepper.
Coat each baking-powder-coated drumstick thoroughly with the Parmesan-spice mixture, pressing the mixture onto the surface so it adheres.
Lightly spray the air fryer basket with oil and arrange drumsticks in a single layer without overlapping; cook in batches if necessary.
Air fry at 380°F for 24 minutes, flipping the drumsticks halfway through the cooking time.
Increase the air fryer temperature to 400°F and cook an additional 5–6 minutes to crisp the coating.
Remove the drumsticks from the air fryer and let rest for about 5 minutes before serving; confirm internal temperature reaches 165°F with an instant-read thermometer.