Preheat air fryer to 300°. In a small bowl, combine egg and milk. In a small skillet, heat butter until hot. Add egg mixture; cook and stir over medium heat until eggs are completely set. Remove from the heat. Fold in ham and cheese.
Separate crescent dough into 2 rectangles. Seal perforations; spoon half the filling down the center of each rectangle. Fold dough over filling; pinch to seal. Place in a single layer on greased tray in air-fryer basket. Cook until golden brown, 8-10 minutes.