Place each chicken breast on waxed paper.

Carefully flatten chicken using a meat mallet or rolling pin to about 1/4 inch thickness.

Sprinkle both sides of the flattened chicken with salt and pepper.

Place 1/2 slice of ham and 1/2 slice of Swiss cheese on each chicken breast.

Tuck in the sides of the chicken over the ham and cheese.

Roll up the chicken breast jelly roll fashion, ensuring a tight seal.

Secure the rolled chicken with toothpicks to prevent unraveling.

In a shallow bowl, beat the egg and water together until well combined.

In another shallow bowl, combine the bread crumbs, flour, and Parmesan cheese.

Dip each piece of chicken into the egg mixture, ensuring it is fully coated.

Immediately transfer the egg-coated chicken to the bread crumb mixture and coat thoroughly, pressing gently to adhere.

Heat cooking oil in a large skillet over medium-high heat.

Carefully place the breaded chicken rolls into the hot oil, ensuring not to overcrowd the pan.

Brown the chicken on all sides, approximately 6-8 minutes per side, until golden brown and cooked through.

Remove the browned chicken from the skillet and place on a wire rack or paper towel-lined plate to drain excess oil.

Reserve the pan drippings for a potential Creamy Sauce (optional).

Carefully remove the toothpicks before serving.