Press chicken breasts with the palm of your hand to flatten to an even thickness.

Beat egg into a shallow bowl; place bread crumbs into a separate shallow bowl. Dip each chicken breast into beaten egg and press into bread crumbs to coat.

Heat butter in a large skillet over medium heat and fry coated chicken breasts until golden brown, about 5 minutes per side.

Pour pasta sauce over chicken, cover, and bring sauce to a boil. Reduce heat to low and simmer for 10 minutes. Sprinkle chicken with mozzarella cheese, Parmesan cheese, and parsley. Cover and simmer until cheeses melt, about 5 more minutes.