Preheat oven to 375°F (190°C) and lightly grease a baking dish.
Butterfly chicken breasts and pound to even thickness.
Season chicken with salt, pepper, and garlic powder.
Layer ham and Swiss cheese inside each breast and roll tightly.
Secure with toothpicks if needed.
Dredge chicken in flour, dip in beaten eggs, then coat with breadcrumbs.
Place in baking dish, drizzle with olive oil or butter, and bake 25–30 minutes until internal temperature reaches 165°F (74°C).
Optional sauce: melt butter, whisk in flour, add milk, cook until thick, stir in parmesan, and serve over chicken.