Combine milk, sugar, rice, water and salt in a heavy 4 quart saucepan. Bring to a boil.
Reduce heat and simmer, uncovered, 50-60 minutes, until rice is tender. Stir frequently during cooking to keep from sticking to bottom of pan. Remove from heat.
Stir in beaten eggs and vanilla. Pour into 1 1/2 quart baking dish. Sprinkle with cinnamon. May be served warm or chilled with added milk or whipped cream. Yields 6 servings.