Set up the breading station. In three shallow dishes, add flour, beaten egg in the second one, and combine breadcrumbs and grated parmesan cheese in the last.
Prep the chicken. Place the chicken on a cutting board. Make a horizontal slit on the side of each chicken breast for a butterfly cut.
(Optional) Pound the chicken to make it thinner. Cover the chicken with plastic wrap. With a meat mallet (or a rolling pin), gently pound the chicken until it reaches a 1/2-inch thickness.
Season the butterflied chicken breasts with salt and pepper, ensuring both sides are evenly coated.
Add 2 slices of ham and 2 slices of Swiss cheese to each chicken breast. Roll up the chicken and secure it with toothpicks to seal the edges.
Preheat your air fryer to 380ºF (193ºC).
Bread the chicken. Dip each chicken into the flour, shaking off excess. Next, dip into the beaten egg. Finally, transfer the chicken to the breadcrumb mixture, pressing the breadcrumbs to adhere.
Place the breaded chicken breasts in the air fryer, ensuring they don't overlap. Spray the breaded chicken breasts with avocado oil.
Air fry cordon bleu at 380ºF (193ºC) for 20 - 25 minutes, flipping them halfway through for even cooking. Then, spray with more avocado oil, so both sides will be golden brown.
Make the creamy dijon sauce. In a small saucepan, melt the butter over medium heat. While constantly stirring, add in the flour and cook for about 1 minute. Pour the milk while whisking to prevent lumps. Add Dijon mustard and cook until it thickens.
Check the internal temperature of the cordon bleu using a meat thermometer to ensure it's fully cooked (165°F or 74°C). Then, remove from the air fryer and remove the toothpicks.
Serve and enjoy the Air Fried Chicken Cordon Bleu with the creamy Dijon mustard sauce drizzled on top.