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 cinnamon sticks and return 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.
Make Ahead: Just store in the refrigerator in an airtight container for a few days. We reheat it in a pot and add a bit more cinnamon to the top before serving.Variations: For a more intense cinnamon-flavored rice pudding, add 1 teaspoon of cinnamon in Step 2 when adding the milks. You can also add raisins at this point, if you wish.Toppings: Try topping each serving with a sprinkle of brown sugar, nutmeg or coconut or with a drizzle of honey.