Preheat your oven to 375°F.
Place each chicken breast between two sheets of plastic wrap and pound them to about ½ inch thick using a meat mallet or rolling pin.
Season both sides of the chicken with salt, pepper, garlic powder, onion powder, and paprika.
Lay two slices of ham and two slices of Swiss cheese on each chicken breast.
Roll the chicken tightly, starting from the narrow end, and secure with toothpicks if necessary.
Set up a breading station: Place flour in one shallow dish, beat the eggs in a second dish, and combine breadcrumbs with a pinch of salt and pepper in a third dish.
Dredge each chicken roll in flour, dip in the beaten eggs, and coat with breadcrumbs, pressing gently to adhere.
Heat the vegetable oil in a large skillet over medium heat. Once hot, add the chicken rolls and cook for about 4-5 minutes on each side until golden brown.
Transfer the browned chicken to a baking dish and bake in the preheated oven for 20-25 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F.
Remove from the oven, let rest for a few minutes, then remove toothpicks and slice to serve.