Prepare the Chicken:
On a cutting board, use a sharp knife to remove the tenderloin from the back of each chicken breast (reserve for another use). Slice each breast horizontally, stopping about 1/2 inch (1 cm) from the edge to create a "book" shape. Open the chicken like a book and place it between two pieces of plastic wrap. Lightly pound the breasts with a mallet until evenly flattened. Remove the top plastic wrap.
Stuff the Chicken:
Spread half the Dijon mustard on one side of each breast. Layer 2 slices of ham and 2 slices of Swiss cheese on top. Fold the chicken breast over the filling and secure it with toothpicks. Repeat with the second breast and remaining ingredients.
Coat the Chicken:
Place the flour in a shallow dish. In another dish, lightly beat the egg. In a third dish, combine the breadcrumbs and Parmesan. Season the stuffed chicken breasts with salt and pepper, then coat each in flour. Dip them into the egg, allowing excess to drip off, and coat them in the breadcrumb mixture, pressing to adhere.
Cook in the Air Fryer:
Spray the air fryer basket with non-stick cooking spray. Place the chicken breasts in the basket and spray them lightly with the cooking spray. Cook at 375°F (190°C) for 15 minutes or until golden brown and cooked through. (The stuffed chicken can be stored for up to 3 days in the refrigerator or 1 month in the freezer.)
Serve:
Remove the toothpicks and slice the chicken into portions. Serve with creamy mustard sauce and, if desired, a side of green vegetables or a crisp salad.