Cut the ends from the zucchini, peel, and cut into strips about 1 inch wide, 4 inches long, and ¾ inch thick. Mix salt and pepper with the beaten eggs. Heat cooking oil in a large skillet until hot. Mix the cheese and breadcrumbs. Dip the slices of zucchini in the egg, then the breadcrumb mixture, and brown on all sides. Turn gently to avoid breaking the slices. Add more cooking oil if necessary. Remove to a heated platter, sprinkle with parsley and serve as is, or with a tomato sauce.