Beat eggs with milk. Add 1/2 cup grated cheese and parsley. Dip chicken pieces in egg mixture and roll in bread crumbs. Lightly brown in a skillet with a bit of olive oil. Remove to a baking dish.
Over medium heat, melt butter. Add cream and milk, stirring constantly. Add cheese and parsley until it is a warm sauce.
Pour sauce over chicken breasts. Cover with foil and bake at 350° for 20 to 30 minutes or until chicken is cooked. During the last five minutes, add a slice of mozzarella to each bread piece and allow to melt.