Place each chicken breast between two pieces of plastic wrap and gently pound it until it’s about ¼ inch thick all over. Season both sides with salt, black pepper, and dried oregano. Top each breast with 2 slices of ham and 2 slices of Swiss cheese, then roll it up tightly. Secure each roll with toothpicks to keep the filling in place while cooking.

Set up three shallow bowls one with flour, one with beaten eggs, and one with breadcrumbs. Roll each stuffed chicken breast in the flour, making sure it’s lightly coated. Dip it into the beaten eggs, then finish by covering it evenly with breadcrumbs, pressing gently so the coating sticks well.

Heat butter or oil in a large oven-safe skillet over medium heat. Add the breaded chicken rolls and cook for 2 to 3 minutes on each side until they’re nicely golden. Transfer the skillet to a preheated 375°F (190°C) oven and bake for 20 to 25 minutes, or until the chicken is fully cooked and reaches an internal temperature of 165°F (74°C).

While the chicken is baking, melt the butter in a saucepan over medium heat. Stir in the flour and cook for about a minute to form a smooth base. Slowly whisk in the milk until the mixture is lump-free. Let it simmer for 3 to 5 minutes until it thickens, then stir in the Dijon mustard, Parmesan cheese, Worcestershire sauce, salt, and black pepper. Mix until the sauce is smooth, rich, and creamy.

Once the chicken is done, remove it from the oven and let it rest for about 5 minutes. Carefully take out the toothpicks, then slice each roll into thick pieces if you like. Resting the chicken helps keep the cheese filling warm and prevents the juices from escaping.

Place the Chicken Cordon Bleu on serving plates and spoon the warm Dijon Parmesan sauce generously over the top. Pair it with creamy mashed potatoes, roasted asparagus, steamed green beans, mixed vegetables, or a crisp garden salad for a delicious, well balanced meal.