Combine the rice, cinnamon sticks, and water in a large pot over medium-high heat. Bring to a boil uncovered.
Lower the heat to maintain a medium boil and continue cooking, uncovered, for 16-18 minutes. Stir and scrape the sides of the pot occasionally, until the rice is tender and most of the liquid has been absorbed.
Drain any remaining liquid, if needed. Remove the cinnamon sticks. Add the sweetened condensed milk, evaporated milk, whole milk, and ground cinnamon to the pot. Bring to a boil.
Reduce the heat to low and cook for about 20 minutes, stirring and scraping the sides and bottom of the pan constantly. The milk mixture can easily burn, so it's important to stir constantly as it thickens.
Scoop into individual bowls and sprinkle each serving with additional cinnamon, if desired.