Preheat the air fryer to 350°F (175°C) for 3 minutes.
Unroll the crescent dough and separate it into triangles.
Place one slice of ham and one slice of cheese on each triangle.
Roll each triangle from the wide end toward the tip, enclosing the filling.
Brush each roll-up with the beaten egg.
Mix the melted butter, garlic powder, onion powder, and Italian seasoning in a small bowl.
Brush the seasoned butter over the tops of the roll-ups.
Sprinkle with sesame seeds or everything bagel seasoning if desired.
Arrange the roll-ups in a single layer in the air fryer basket, leaving space between each one.
Air fry for 8 to 10 minutes, or until the dough is golden brown and the cheese is melted.
Allow to cool for 2 to 3 minutes before serving.