Preheat oven to 350 degrees. Put a layer of soup on the bottom of a 9x12 baking dish, then add a layer of spaghetti, add more tomato soup, some of the ground ham and grated cheese. Add more spaghetti, more soup, ham and cheese until you use up the first four ingredients.
Beat the eggs and combine them with the milk. Pour the mixture over the top, poking holes here and there to allow egg mixture to distribute throughout the dish. Bake the casserole for 25-30 minutes or until the dish "sets". Cut into serving portions.