Gather the ingredients.

Place a chicken breast on a flat work surface. Slice horizontally through the middle, being careful not to cut all the way through to the other side. Open the 2 sides and spread them out like an open book. Place chicken breast between 2 sheets of heavy plastic on a solid, level surface; lightly pound with the smooth side of a meat mallet to a 1/4-inch thickness. Repeat with remaining chicken breast.

Season each chicken breast with salt and pepper. Spread Dijon mustard on top. Place 1 slice of cheese on each breast. Top each with 2 slices of ham and 1 slice of cheese. Roll each breast up and secure with a toothpick.

Place flour in a shallow bowl. Place egg in a second bowl. Mix panko bread crumbs and grated Parmesan in a third bowl. Preheat an air fryer to 350 degrees F (175 degrees C).

Meanwhile, dredge chicken breasts in flour; shake off excess. Dip into beaten egg, allowing any excess egg to drip back into the bowl. Press into bread crumb mixture to coat both sides; place breaded chicken breasts onto a plate and spray with nonstick spray. Let sit for 5 minutes while the air fryer preheats, then arrange breaded chicken in a single layer in the air fryer basket.

Cook in the preheated air fryer for 10 minutes; flip chicken breasts and spray any dry spots with nonstick spray. Cook until chicken is no longer pink in the center, 8 minutes more. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).