Pour the rice, cinnamon sticks, and 2 cups of the water into the bowl of a blender. Blend until the rice & cinnamon is roughly ground, about 1 minute. Pour the remaining 3 cups of water in & blend for another 1-2 minutes. Let sit at room temperature for a minimum of 4 hours.

Strain the rice water into a pitcher and discard the solids. Stir the milk, vanilla, cinnamon, and sugar into the rice water. Chill and stir before serving.