Place the chicken breasts between two sheets of plastic wrap and pound them to an even thickness using a meat mallet. Season both sides with salt, pepper, garlic powder, and paprika.
Lay a slice of ham and Swiss cheese on each chicken breast. Carefully roll the chicken, tucking in the sides, and secure with toothpicks.
Dredge each rolled chicken breast in flour, then dip in the beaten eggs, and finally coat with breadcrumbs. Press the breadcrumbs gently to ensure an even coating.
Preheat the oven to 375°F (190°C). Place the breaded chicken on a baking sheet lined with parchment paper. Drizzle with melted butter and bake for 25 minutes, or until golden brown and cooked through.
Let the chicken rest for 5 minutes before slicing. Serve with a side of your favorite vegetables or a creamy Dijon sauce.