In a skillet saute' chopped onions in oil. Add tomato puree, water, salt, oregano and pepper. Bring to a boil and simmer for 15 minutes. In a greased baking dish alternate thin layers of sliced eggplant, tomato sauce and half of the grated cheese, starting with layer of eggplant and ending with layers of tomato sauce. Bake in moderate oven (350 deg) for 1 hour. Minutes before removing from oven, sprinkle remaining grated cheese over top and continue heating until cheese melts.