Flatten cutlets to 1/4-inch thickness, using a meat mallet or rolling pin. Cut into serving size pieces. Sauté cutlets in oil in a large skillet until browned; remove from skillet, and set aside. Reserve oil in skillet.
Add onion, mushrooms, and garlic to skillet; sauté until tender. Add flour, salt, and pepper, stirring well. Cook 1 minute, stirring constantly. Add wine, and cook over medium heat until thickened.
Return cutlets to skillet; pour water over cutlets. Cover and cook over low heat 45 minutes or until veal is tender.
Transfer veal to a serving dish; pour mushroom gravy over top. Sprinkle with parsley, if desired.