Combine water, rice, and cinnamon sticks in a large saucepan over medium-high heat. Bring to a boil, uncovered, and cook for 16–18 minutes.
Drain any remaining liquid, remove the cinnamon sticks, and return the rice to the pan over medium-high heat. Add sweetened condensed milk, evaporated milk, and whole milk, and bring to a boil.
Reduce the heat to low and cook for about 20 minutes, stirring constantly. The milk can easily burn, so it is important to stir constantly as it thickens.
Divide rice among serving cups and sprinkle with cinnamon. Serve warm.
