Soak rice in cold water for 20 minutes, rinse well.
In a large sauce pan add rice and cover with cold water.
Bring to a boil, lower the heat to simmer until water evaporates.
In another small saucepan heat milk on medium high heat, add the rice to the milk and continue to cook the rice until soft, stirring often, making sure the rice does not stick to the bottom of the pan.
Add the sugar stirring gently so the sugar slowly dissolves.
Remove from heat and allow to cool for 15-20 minutes.
In a separate bowl, beat eggs well and stir in 1 cup of the cooled rice mixture to tmper the mixture.
Pour the tempered mixture back into the pot, over low heat.
Gently stir in 1/2 cup of heavy cream, cooking for about 15 minutes.
Remove from heat and stir in the vanilla and cinnamon stick.