Butterfly the chicken breasts and pound them to an even thickness.
Season the chicken breasts with Chud's Barbecue poultry rub.
Layer Swiss cheese, ham, Gruyere cheese on the chicken breasts and roll them up tightly.
Wrap the rolled chicken breasts in plastic wrap and chill in the freezer.
Prepare the sauce by making a roux with butter and flour, then adding milk, nutmeg, Dijon mustard, Parmesan cheese, salt, and black pepper.
Grill the rolled chicken breasts over charcoal until cooked through.
For the deep-fried version, coat the rolled chicken breasts in flour, egg wash, and panko breadcrumbs, then deep fry until golden brown.
Serve the grilled and fried chicken cordon bleu with the sauce drizzled on top and garnish with parsley and flaky salt. Enjoy!
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