Rinse the rice under cold water in a colander.

Combine rice, cinnamon sticks, and 4 cups of water in a bowl. Cover and refrigerate overnight or for at least 4 hours.

Remove most of the cinnamon sticks, keeping some small pieces with the rice.

Blend the rice with half of the water and remaining cinnamon in two batches until smooth, about 4 minutes.

Pour the blended mixture through a fine strainer or cheesecloth into a pitcher, pressing solids to extract liquid.

Repeat with the remaining rice mixture and water.

Stir in the canned milks, optional vanilla, and remaining 4 cups of water. Mix until well combined.

Taste and add sugar or more water to adjust flavor. Chill and stir before serving over ice.