Pound the chicken filets to ¼” thick by placing a sheet of plastic wrap under and over the top and pounding with a meat mallet.
Remove the top layer of plastic wrap. Season the chicken filets with half the salt.
Place 2 slices of ham and Swiss cheese over the top of the chicken. Roll the chicken tightly using the plastic wrap that’s under the chicken to form a tight roll. Secure the wrap around the chicken and put it in the refrigerator for 30 minutes to firm up. If the roll doesn’t stay together, use a toothpick to secure it.
Place 3 tablespoons of flour on a shallow plate along with the onion and garlic powders, beat the egg in a bowl, and place the breadcrumbs on another plate.
Remove the chicken from the plastic wrap. Roll it first in the flour, then the egg, then the breadcrumbs.
Place the breaded chicken into the air fryer basket. Spray evenly with cooking spray.
Cook at 380 degrees F for 22 to 25 minutes, turning 2-3 times during cooking to prevent burning, until the internal temperature reaches 165 degrees F on a meat thermometer.
To make the sauce, melt the butter in a saucepan over medium heat. Once melted, add the remaining ½ tablespoons of flour and whisk to combine. Cook for 30 seconds, whisking constantly.
Pour in the milk and Dijon mustard, whisk until the sauce is thickened. Add the remaining salt and Swiss cheese and let it melt into the sauce. If the sauce is too thick, add additional milk or water to thin it.
Slice the chicken and serve with the sauce poured over the top.
Notes
Check the chicken with a meat thermometer in the last few minutes of cooking to make sure it reaches an internal temperature of 165 degrees F (74 degrees C).
If the chicken is getting too dark, turn down the heat on the air fryer.
All air fryers have different wattage and may cook at different rates. You may need to adjust the time or temp for the best results.