1. Preheat your oven to 375°F (190°C). Lightly grease a baking dish with olive oil or cooking spray.
2. Place each chicken breast between two sheets of plastic wrap. Use a meat mallet to gently pound each breast to about 1/2 inch thickness.
3. Season the chicken breasts with salt and pepper on both sides.
4. Lay 2 slices of ham and 2 slices of Swiss cheese on each chicken breast. Roll each breast tightly, securing it with toothpicks if necessary.
5. In a shallow dish, combine the breadcrumbs, Parmesan cheese, garlic powder, paprika, salt, and pepper.
6. Set up a breading station with three dishes: one with flour, one with beaten eggs, and one with the breadcrumb mixture.
7. Dip each chicken roll first in flour, then in egg, and finally coat with the breadcrumb mixture, pressing gently to adhere.
8. Place the coated chicken rolls in the prepared baking dish and drizzle with olive oil.
9. Bake in the preheated oven for 25-30 minutes, or until the chicken is cooked through and the coating is golden brown.
10. Let the chicken rest for a few minutes before slicing. Garnish with fresh parsley if desired.

Remember, the key is to not rush the rolling process. Take your time to ensure the fillings are well-contained within the chicken for that perfect, melty center.