Preheat your oven to 375°F (190°C). Place the chicken breasts between two pieces of plastic wrap and pound them to about 1/2 inch thick. Season both sides with salt, pepper, and garlic powder.

Assemble the Cordon Bleu

Place 2 slices of ham and 2 slices of Swiss cheese on each chicken breast. Fold the chicken over to enclose the filling, and secure with toothpicks if necessary.

Bread the Chicken

Set up a breading station with three plates: one with flour, one with beaten eggs, and one with breadcrumbs. Dredge each stuffed chicken breast in flour, dip in egg, and coat with breadcrumbs.

Cook the Chicken

In a large skillet, heat butter and olive oil over medium heat. Add the breaded chicken breasts and cook for about 4-5 minutes on each side until golden brown. Transfer to a baking dish and finish cooking in the oven for 15-20 minutes.

Prepare the Cordon Bleu Gravy

In the same skillet used for the chicken, add chicken broth and scrape up any browned bits. Stir in heavy cream and simmer for about 5 minutes until thickened. Adjust seasoning with salt and pepper to taste.

Serve

Slice the cooked chicken Cordon Bleu and drizzle with gravy. Garnish with parsley before serving.