Preheat oven to 375°F (190°C). Place each chicken breast between plastic wrap and pound to 1/4-inch thickness using a meat mallet.

Season both sides of the chicken with salt, black pepper, and paprika. Place a slice of ham and a slice of Swiss cheese on each chicken breast.

Roll up each chicken breast tightly, securing with toothpicks if necessary. Dredge each roll in flour, shaking off excess.

Dip each floured chicken roll into the beaten eggs, then coat evenly with breadcrumbs.

Heat butter and olive oil in a large oven-safe skillet over medium heat. Brown the chicken rolls on all sides, about 2-3 minutes per side.

Transfer the skillet to the preheated oven and bake for 15-20 minutes, or until the chicken is cooked through and the cheese is melted.

Remove toothpicks before serving. Let rest for 5 minutes, then slice and serve.