Add uncooked rice, cinnamon sticks and 2 cups of water to a blender and blend for 2 minutes. Add 2 more cups of water and blend again until the cinnamon sticks and rice are finely ground.
Pour into a large pitcher or other tall container with a tight fitting lid and let soak for at least 6 hours or overnight.
Using a cheesecloth or a fine mesh strainer, strain the mixture into a large pitcher. Discard the rice.
To the pitchers, stir in sugar and milk until sugar is dissolved. Pour horchata over ice in glasses. Sprinkle cinnamon on top for garnish.
Notes
Ground cinnamon is sometimes used but doesn't have the same taste. Cinnamon sticks are highly recommended.