1. Mix together the mashed potatoes, egg, flour, kosher salt, garlic powder, parmesan cheese, and butter in a mixing bowl until blended well.
2. Scoop mixture to make small mounds of the potato mixture and flatten to make 1/2-inch thick patties.
3. Place the potato cakes in a baking dish that can fit into your Air Fryer basket. Set your Air Fryer to 400 F (200 C) and then cook for 25 minutes or until they browned.