In a plastic freezer bag, or under a sheet of plastic wrap, pound chicken breasts to 3/8" to 1/2".
Cut each chicken breast into 3 equal-sized pieces and lightly season with kosher salt and black pepper.
Drench these chicken cutlets in flour, shaking off the excess.
Dip the chicken in the beaten egg and cover completely.
In a dish with the bread crumbs mixed with 1 tsp kosher salt, coat all sides of the chicken.
Heat peanut oil in a pan; hot but not smoking.
Place chicken in the pan and cook for 5 minutes, flipping once halfway through.
Blot excess oil off the cooked breaded chicken breasts with paper towels.
(For a healthier baked chicken parmesan, you can skip the frying and bake them for 25 minutes at 450 degrees.)
Place chicken on a cookie sheet and top with mozzarella cheese.
Place in broiler and cook until cheese is bubbly.
Spoon the pasta sauce over the chicken and garnish with parmesan cheese and parsley.