Place the 12 chicken drumettes in the air fryer basket in a single layer (use parchment if desired) and cook for 8 minutes.
Flip the drumettes and cook for another 8 minutes, then check for crispness and doneness; if needed, cook an additional 2 minutes.
While the chicken cooks, melt the 2 tablespoons butter with the 2 tablespoons olive oil in a 12-inch skillet over medium heat, then add the 2 tablespoons minced garlic and cook until fragrant (about 30–60 seconds).
Remove the skillet from heat and stir in the 1/3 cup grated Parmesan and 1 tablespoon minced parsley until combined.
Transfer the cooked drumettes to the skillet and toss gently to coat them evenly in the garlic-Parmesan sauce.
Serve the wings hot.
Notes
You can melt the butter and heat the olive oil in the microwave instead of using the stovetop.