Preheat the oven to 375°F (190°C) if you are baking the chicken.
Place each chicken breast between two pieces of plastic wrap. Use a meat mallet or rolling pin to gently pound the chicken to about ½ inch thickness.
Lay 1 slice of ham and 1 slice of Swiss cheese on top of each flattened chicken breast.
Carefully roll each breast tightly from the bottom up, keeping the filling secure inside. Use toothpicks or kitchen twine to secure the ends.
Prepare three shallow bowls: one with flour mixed with salt, pepper, garlic powder, and paprika; one with beaten eggs; and one with breadcrumbs.
Dredge each chicken roll first in the flour mixture, shaking off the excess, then dip it in the egg wash, and finally coat it with breadcrumbs, pressing gently to adhere.
If baking, place the breaded chicken rolls on a greased baking sheet and bake for 25-30 minutes, or until fully cooked (internal temperature reaches 165°F/74°C). If frying, heat oil in a frying pan over medium heat and cook each roll for about 6-7 minutes per side, or until golden brown and cooked through.
Remove toothpicks or twine before serving. Slice the rolls to reveal the ham and cheese inside.