The secret to the crunchiest, gooiest, air-fryer grilled cheese EVER is first mixing softened butter with Italian seasoning and Parmesan cheese and then spreading it on the outside of your bread. You can't get results like these from a pan!
First, combine the room temperature butter, grated Parmesan, and Italian seasoning in a bowl. Then, spread the butter mixture over one side of each piece of bread, from edge to edge.
Place the sliced cheese between the two pieces of bread, buttered sides facing out.
Preheat the air fryer (if yours does not have a preheat setting, let it run for about four minutes at 400ºF).
Finally, place the sandwich in the air fryer basket. Cook at 350ºF for five minutes, then flip and cook for 5 minutes on the other side, or until golden brown and crispy and the cheese is melted through. Slice and serve.