Cook rice in water according to package directions. Rice should be soft.
Add milk to rice in saucepan and heat over medium low heat.
Add sugar and stir, continuing to heat mixture and dissolve sugar.
Beat eggs in a heatproof bowl, then beat in cornstarch.
Scoop about 1/2 c. of rice/milk/sugar mixture into eggs, stirring with a fork to thoroughly mix.
Pour egg mixture back into rice/milk/sugar in saucepan.
Turn heat up to medium and cook rice pudding until mixture begins to boil steadily, using a whisk to keep the pudding moving in the pan so that it doesn't burn.
Turn heat off and stir in vanilla. Pour pudding into large bowl or individual serving bowls. Sprinkle liberally with cinnamon. Cool.
Keep leftovers in refrigerator.