Cook rice in water. Combine rice, water, and cinnamon sticks in a large (5 quart) saucepan or Dutch oven. Bring to a boil, then reduce heat to a simmer and cook 5 minutes. Stir occasionally to dislodge any rice stuck to the bottom.
Add milks. Add evaporated milk, sweetened condensed milk, and salt and bring to a boil over medium heat (be careful not to let it boil over). Turn the heat to medium-low or low so that the milk mixture is gently simmering and cook uncovered until the rice is tender. Start checking after 20 minutes but it could take as long as 30 minutes. Stir frequently to prevent rice from sticking to the bottom.
Serve. Once rice is tender, remove immediately from the heat. It's okay if it is soupy, it will thicken as it sits. Cover and let cool 30 minutes to thicken up. Remove the cinnamon sticks and serve warm, room temperature, or cold with sliced strawberries or a dusting of ground cinnamon.