Place the rice in a colander and rinse under cold water. Place the rice, cinnamon sticks, and 4 cups of water into a bowl. Cover the bowl and refrigerate overnight or a minimum of 4 hours.

Once ready to blend, remove most of the cinnamon sticks but leave small pieces with the rice.

Blend the rice in two separate batches, adding 1/2 of the rice and water with some cinnamon stick left behind. Puree until very smooth and forms a watery paste-like texture, about 4 minutes.

Using a very fine strainer or cheesecloth, pour the blended mixture over a pitcher. Strain out as much liquid as possible, pushing on the solids with a spatula or spoon.

Repeat this process for the rest of the rice, water, and cinnamon mixture.

Stir in the canned milks, vanilla, and the additional 4 cups of water. Stir well until everything is incorporated.

Taste and add sugar or water if needed according to taste.

Chill and stir well before serving over ice.