Preheat air fryer to 380 degrees F (175 degrees C).
Spread ½ teaspoon butter on each slice of bread. Place 1 slice of bread, butter side down in the air fryer. Top with 2 slices cheese. Place 2nd slice of bread, butter side up, over cheese.
Air-fry until golden brown, 3 to 4 minutes. Flip sandwich over and air-fry an additional 1 to 2 minutes.