Prep the Chicken: Place the chicken breasts on a cutting board, ensuring they are flat. Generously season both sides with salt, pepper, garlic powder, and onion powder. With care, create a pocket in each breast by slicing into the meat without cutting all the way through.
Stuff the Chicken: Place four slices of Swiss cheese and a few slices of ham into each pocket. Press the edges of the chicken gently to close the pockets.
Set Up Breading Stations: Place the flour in one bowl, the beaten eggs in another, and the panko breadcrumbs in a third.
Bread the Chicken: Dredge each stuffed chicken breast in flour, shaking off excess. Dip into the beaten eggs, then coat generously with panko breadcrumbs.
Fry the Chicken: Heat about ½ inch of oil in a large skillet over medium-high heat. Fry each chicken breast for about 4–5 minutes per side until golden brown and cooked through.
Make the Roux: In a medium saucepan over medium heat, melt the butter. Stir in the minced garlic and cook for approximately 1 minute, allowing it to become fragrant and golden.
Thicken the Sauce: Stir in the flour to create a roux and cook for about 1 minute.
Add the Flavor: Stir in Dijon mustard, Parmesan cheese, salt, and pepper. Keep whisking the mixture as it simmers, allowing the sauce to thicken for about 5 minutes.
Serve: Pour the warm Dijon sauce over the fried Chicken Cordon Bleu and garnish with fresh herbs if desired.