Combine water, rice and salt in a 2 to 2 1/2 cup microwave-safe bowl. Cover. Microwave on HIGH for 5-6 minutes or until mixture boils. Let stand, covered, for 10 minutes. Microwave on HIGH for an additional 4-5 minutes, or until rice is tender. Transfer to a large (12 cup) microwave-safe container.
Stir in the butter, sugar and milk. Cover. Microwave on HIGH for 8-10 minutes or until mixture boils. Beat the eggs and blend in a small amount of the hot mixture into the eggs, beating well. (This will prevent the eggs from curdling). Return to the large container, blending in well.
Microwave on HIGH, uncovered, 1 to 1/2 minutes, or until mixture bubbles around the edge, stirring once.
Stir in vanilla and transfer to serving dish; sprinkle with cinnamon, if desired. Cool - pudding will thicken as it cools. Serve warm or chilled.
Note1: Microwave ovens vary considerably in power. Watch carefully the first time you make this and note the times needed in your microwave oven. My current microwave is 1200 watts. I set it to power setting 6, which is 60% of full strength or equivalent to 720 watts. I then just follow the original timing. If you calculate whatever power setting gets you closest to 700 watts, you can do the same.
Note2: I use a microwave popcorn popper to cook this - it works beautifully. Be sure your container is big - you don't want this boiling over in your microwave!