Preheat oven to 350 degrees F
Boil water, then take it off the stove-top fire
Pour in the rice, stir, cover it and let it sit for 10 min
While waiting, mix together eggs, sugar, and vanilla in a giant bowl.
Add in the cooked, hot, rice, plus the butter (it will melt from the heat of the mixture) then stir everything together well, making sure the butter is fully melted and mixed in.
Add in the milk, and stir well. The mixture should look soupy at this point.
Pour the mixture into a butter-coated or pam-sprayed 9 x 11 pyrex baking pan.
Heavily sprinkle the cinnamon (or cinnamon sugar) over the mixture in the pan. It should be completely covered! Note: the original recipe called for straight cinnamon but when I made it the first time, I didn't have any on hand so we used cinnamon sugar and it was amazing too! If you like really sweet, go the cinnamon sugar route.
Put it in the oven for 40-50 min in your preheated 350 degrees F oven. Check for browning around the edges and also stick a toothpick in the pudding for doneness.
Let it cool by allowing it to sit out for at least an hour before putting it in the refrigerator for 5-6 hours or overnight, with a lid on your Pyrex dish (foil works too!).
Take out the rice pudding dish from the refrigerator when it's fully cold and cut it into squares.
Put them onto a platter and serve cold!