Preheat your air fryer by running it at 400℉ (200℃) for 5 minutes.
Cut the potatoes by placing a potato in a wooden spoon, and slicing into it with a sharp knife. Make cuts as close together as possible, at least every ⅛ inch (3 mm). Make sure the cut does not go all the way through the potato, you want it to be intact at the bottom - the wooden spoon will help achieve this.
Melt butter and mix with garlic powder, salt and ground black pepper. Pour over the potatoes and gently mix to coat, using a pastry brush if needed. Save the leftover melted butter mix for later.
Place the potatoes in the air fryer basket and air fry 15 minutes at 400℉ (200℃), until they are cooked almost or all the way through.
Brush the potatoes with the remaining butter mixture, then top with parmesan and air fry 4-5 more minutes at 400℉ (200℃). Keep a close eye on the potatoes so they don't burn - I recommend removing the air fryer basket to check a few times while cooking.
