Preheat the air fryer to 340°F (170°C).
Spread butter on one side of each slice of bread.
Place the cheddar cheese and Monterey Jack cheese between the bread slices, with the buttered sides facing outward.
Lightly spread additional butter over the outside surfaces of the sandwich.
Secure the sandwich with a toothpick through the center to prevent it from shifting during cooking.
Place the sandwich in the air fryer basket.
Cook the Air Fryer Grilled Cheese for 8 minutes, flipping halfway through cooking.
Remove when both sides are golden brown and the cheese is fully melted.
Serve immediately while hot and crispy.