Pat the wings dry with paper towels to remove excess moisture; this helps them crisp in the air fryer.
Place the wings in a mixing bowl, drizzle with 1 tablespoon olive oil, and season with salt and black pepper to taste; toss to coat evenly.
Sprinkle the garlic powder and grated Parmesan over the wings and toss until the wings are well coated.
Arrange the wings in a single layer in the air fryer basket with minimal overlap; cook at 375°F (190°C).
Air-fry the wings for 22–26 minutes, tossing or shaking the basket 2–3 times during cooking, until they are crispy and reach an internal temperature of 165°F (74°C).
Transfer the wings to a serving plate, garnish with additional grated Parmesan and minced parsley if desired, and serve with sliced carrots, celery, and ranch dressing.