Preheat your air fryer to 370°F (188°C) for 3 minutes, which allows it to reach the proper cooking temperature.
Spread 1 tablespoon of softened butter evenly on one side of each bread slice, ensuring complete coverage for even browning.
Flip one bread slice over and place the cheddar and American cheeses evenly on the unbuttered side, then top with the second bread slice with the buttered side facing outward.
Lightly spread the mayonnaise on the top outer surface of the sandwich, which will create an exceptionally crispy and golden crust during cooking.
Carefully place the sandwich in the air fryer basket, mayonnaise-side up, ensuring it lies flat without overlapping other items.
Air fry for 5-6 minutes, then carefully flip the sandwich using tongs, and cook for an additional 3-4 minutes until the bread is golden brown and crisp and the cheese is fully melted.
Remove the sandwich from the air fryer, let it rest for 1 minute on a cutting board to allow the cheese to set slightly, then slice diagonally and serve immediately.