Preheat oven to 250°F.
Arrange a piece of the chicken between two pieces of plastic wrap. Pound out with a mallet until about 1/4-inch thick and repeat with remaining pieces of chicken.
Arrange the beaten egg, flour and breadcrumbs mixed with the cheese in three separate shallow dishes. Season all the pounded chicken pieces with salt and pepper. Working with one piece of chicken at a time, place in the flour then the egg and finally the breadcrumb-cheese mixture. Reserve coated cutlets on a plate and repeat with the remaining chicken pieces.