Place each chicken breast between two sheets of plastic wrap and pound to an even 1/2-inch thickness. Season both sides with salt and pepper.
Layer 2 slices of ham and 1 slice of swiss cheese on each chicken breast. Roll each breast up tightly, tucking in the sides, and secure with toothpicks.
Set up a breading station: flour in one shallow dish, beaten eggs mixed with dijon mustard in a second dish, and panko breadcrumbs combined with grated parmesan and garlic powder in a third dish.
Roll each chicken bundle in flour, then dip in egg mixture, then press firmly into the panko mixture to coat completely on all sides.
Preheat the air fryer to 370F. Spray the basket with cooking spray and place the chicken rolls seam-side down, leaving space between each. Lightly spray the tops with cooking spray. Air fry for 18-20 minutes, turning carefully once halfway through, until the outside is deep golden and the internal temperature reaches 165F.
Let rest for 3-4 minutes, remove the toothpicks, then slice each roll in half on a diagonal and serve.