Preheat your oven to 375 degrees F.
On a cutting board, using a meat mallet, pound each chicken breast until they are evenly flattened to about 1/4 inch thickness.
Layer 2 ham slices and 2 slices of cheese on each chicken breast.
Roll each chicken breast tightly, tucking in the sides as you go, and secure with toothpicks. I don't alway use toothpicks. I find if I roll them tightly and place them seam side down in frying pan, they seal.
In a shallow bowl, mix together flour, salt, and black pepper.
In another shallow bowl, beat the eggs.
In a third shallow bowl, place the breadcrumbs.
Now that you have your breading station set up, dip each chicken breast in the flour mixture, shaking off any excess.
Next, dip each chicken breast in the flour mixture then in the egg mixture, and then coat in breadcrumbs.
Heat the oil in a large skillet over medium heat. Add the chicken breasts seam side down and cook until golden brown on all sides, about 3-4 minutes per side.
Transfer the chicken breast to a baking dish or a rimmed baking sheet lined with parchment paper and bake for 20-25 minutes. Until the chicken is cooked through to an internal temperature of 165 degrees Fahrenheit using an instant read thermometer and the cheese is melted.
Remove the toothpicks if using before serving.