In large skillet cook hamburger and onion until meat is lightly browned and onion is tender. Drain off fat. Stir in green beans, tomato soup, water, salt and pepper. Place mixture in greased deep dish 10-inch pie pan or something similar. Prepare potatoes according to directions on box, except do not add the milk. Add beaten eggs and cheese, stir in a little milk if necessary to make potatoes fluffy. Drop potatoes in mounds atop meat mixture. (You can pipe the potatoes on top for a prettier look.) Sprinkle with additional cheese if desired. Bake uncovered at 350 degrees til heated through, 25 to 30 minutes.