Add the white rice, water, and cinnamon sticks to a large bowl.

Cover the bowl and soak the rice mixture overnight in the refrigerator.

Transfer the soaked rice, cinnamon sticks, and soaking water to the blender.

Blend the mixture for 4 minutes until very smooth.

Strain the blended mixture through a fine-mesh strainer into a large pitcher.

Add the granulated sugar and plant milk to the strained cinnamon rice milk.

Add the vanilla sugar, if using, and stir until the sugar dissolves.

Fill 12 serving glasses with ice cubes and pour in the horchata.