In medium size sauce pan over medium-high heat combine soy milk with sugar, vanilla, and cinnamon bring to a boil while constantly stirring.
In a separate bowl large enough to accommodate the hot liquid beat the egg with a whisk while slowly adding the hot liquid a little bit at a time until all of the liquid has been added to the egg.
Place the 2 cups of cooked rice into the pan used to cook the soy milk mixture.
Add the soy milk mixture to the rice in the pan and return heat to medium-high, stir constantly until the mixture comes to a boil then reduce heat to simmer.
Simmer mixture for 15-20 minutes, stirring every 5 minutes until the mixture is a creamy consistency.
Remove from heat, cover top with wax paper and place in the refrigerator to cool.