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Preheat the oven to 350°F (175°C).
Place each chicken breast between two sheets of plastic wrap and gently pound with a meat mallet until about 1/4 inch thick.
Season both sides of the chicken with salt, pepper, and paprika.
On each flattened breast, layer one slice of ham and one slice of Swiss cheese. Roll up tightly and secure with toothpicks.
Set up three shallow dishes: one with flour, one with beaten eggs, and one with breadcrumbs.
Dredge each rolled chicken breast in flour, then dip into eggs, and finally coat with breadcrumbs.
Heat butter and olive oil in a skillet over medium heat. Brown the chicken rolls on all sides until golden, about 3-4 minutes per side.
Transfer the browned chicken rolls to a baking dish and bake for 25-30 minutes until cooked through.
Meanwhile, prepare the sauce by heating heavy cream in a small saucepan. Stir in Dijon mustard and season with salt and pepper. Cook until slightly thickened.
Serve the chicken rolls drizzled with the creamy mustard sauce.
Serving and storage tips:
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