Prepare: Spread softened butter evenly on one side of each bread slice. Shred both types of cheese and combine in a bowl.

Build: Place bread slices butter-side down and distribute cheese mixture evenly on unbuttered sides. Close sandwiches with remaining slices, buttered sides facing out.

Cook: Place in air fryer basket and cook at 375°F / 190°C for 3 minutes. Flip carefully and cook another 3-5 minutes until golden brown and cheese is melted.

Serve: Let rest 1 minute before slicing diagonally. Serve immediately while cheese is hot and melty.