Place the rice in a bowl, cover with hot water. Roughly crumble cinnamon piece into the rice mix and let it all sit and rest anywhere from 2 to 8 hours outside of the refrigerator.
Place half of the rice mixture in the blender with the coconut water and vanilla and blend until smooth, strain into a pitcher or container. Place the other half of the rice mixture in the blender with the milk and the sugar, pure until smooth and strain into the same pitcher or container.
Stir well and serve over ice cubes, or place in the refrigerator until it is cold. Serve with more ice cubes to your liking and sprinkle some ground cinnamon on top if you wish to do so.