Skillet chicken cordon bleu is one of those recipes my whole family loves. You can't beat the creamy sauce, crispy chicken, and smokey ham, all covered in melty Swiss cheese.
Prepare the chicken. Using a meat tenderizer, pound the chicken breasts until they are uniformly about ½ inch thick.
In a bowl, whisk together the egg and milk; in a separate large bowl, whisk together the breadcrumbs, flour, salt, garlic powder, onion powder, and pepper.
Dip each prepared breast first in the egg mixture, allowing any excess to drip off, then coat in the flour mixture. Set the breaded breasts aside.
Heat 2 tablespoons of the olive oil in a large skillet over medium-high heat. Place 2 chicken breasts into the skillet and cook for 4-5 minutes on each side until the chicken is cooked through. Repeat with the remaining two tablespoons of oil and battered breasts.
Remove the cooked chicken from the skillet. Melt the butter in the skillet and whisk the flour into the butter, creating a paste.
Slowly add in the chicken broth and heavy cream, whisking continually to keep the sauce from breaking.
Once the cream and broth are incorporated completely and you have a smooth gravy, add in the Dijon mustard, thyme, salt, and pepper. Whisk to combine, then reduce the heat to low.
Add the chicken back to the skillet in the sauce, and place one slice of ham and one slice of cheese on each chicken breast.
Cover the skillet and cook for about 5 minutes, until the cheese is melted. Remove from heat and serve.
Notes
When adding the liquid to the butter and flour paste, I slowly add about ½ cup at a time, whisking continually until that amount of liquid has been incorporated. Adding liquid in too quickly will break the sauce, which means the paste won’t combine with the liquid.If your skillet is large enough to fry all four chicken breasts at once, you can do that in one step. I like to do it in 2 batches so I can be sure each breast is evenly cooked.