Preheat your oven to 350°F (175°C).
Pound the chicken breasts to about 1/2 inch thickness. Season with salt and pepper.
Place 2 slices of Swiss cheese and 2 slices of ham on each chicken breast. Roll up each breast tightly and secure with toothpicks.
Dredge each chicken roll in flour, then dip in beaten eggs, and coat with breadcrumbs.
Heat the olive oil in a large skillet over medium-high heat. Brown the chicken rolls on all sides until golden brown, about 4-5 minutes per side.
Transfer the browned chicken rolls to a baking dish and bake in the preheated oven for 20-25 minutes, or until the chicken is cooked through.
While the chicken is baking, make the sauce. In a small saucepan, melt the butter over medium heat. Stir in the flour and cook for 1-2 minutes.
Gradually whisk in the milk, continuing to whisk until the sauce thickens. Stir in the shredded Swiss cheese and Dijon mustard. Season with salt and pepper to taste.
Remove the toothpicks from the cooked chicken and serve with the cheese sauce drizzled on top.
Prep Time: 20 minutes | Cooking Time: 30 minutes | Total Time: 50 minutes
Kcal: Approximately 500 per serving | Servings: 4
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