OK, so horchata rice pudding is pretty much like ordinary rice pudding, but a touch more cinnamon-y and still delicious. In the middle of a sweltering, hot summer in Mexico, horchata is often the beverage of choice. This is just another way of serving it, as a dessert.
Combine the rice, milk, and sugar in a pot and bring to a boil, stirring consistently.
Once it comes to a boil, add the cinnamon and vanilla extract. Stir constantly and simmer until most of the rice milk has been absorbed. Let sit, add more sugar and cinnamon, to taste, and serve.