Pour beaten eggs into a shallow dish or bowl. In another shallow dish or bowl, mix together the grated Parmesan cheese and breadcrumbs. Dip chicken breasts into beaten egg, then into breadcrumb mixture to coat.
In a large frypan, heat oil over medium high heat. Add coated chicken and saute for about 8 to 10 minutes each side, or until chicken is cooked through and juices run clear.
Pour tomato sauce into a lightly greased 23x33 inch baking dish. Add chicken, then place a slice of cheese over each breast and bake in the preheated oven for 20 minutes or until cheese is completely melted.