Preheat the oven to 375°F (190°C).
Place each chicken breast between two sheets of plastic wrap. Use a meat mallet to gently pound the chicken to about 1/2-inch thickness.
Season the chicken with salt, pepper, garlic powder, and paprika on both sides.
On one half of each chicken breast, place a slice of ham and a slice of Swiss cheese. Fold the other half over to cover the filling, and secure with toothpicks if necessary.
Set up a breading station: in one shallow dish, place the flour; in another bowl, whisk the eggs; and in a third dish, spread out the breadcrumbs.
Dredge each stuffed chicken breast in flour, ensuring it is fully coated. Dip it into the beaten eggs, allowing any excess to drip off, and finally, coat it in breadcrumbs.
Heat olive oil in a frying pan over medium heat. Add the breaded chicken breasts and cook for about 2-3 minutes on each side until golden brown.
Transfer the browned chicken to a large baking dish and bake in the preheated oven for 20 minutes or until the internal temperature reaches 165°F (74°C).
Remove from the oven and let the chicken rest for a few minutes. Remove toothpicks if used.
Garnish with fresh parsley if desired, slice, and serve warm.