Add rice, almonds and cinnamon sticks to a high speed blender. Blend about 30 - 60 seconds on high speed or until finely pulverized, stopping occasionally and shaking blender if mixture sticks to the bottom.
Pour in 2 cups water, sugar and vanilla. Blend an additional 30 seconds. If your blender can fit the additional liquid pour in remaining 2 cups water, and milk, otherwise pour into a large enough container to fit along with water and milk.
Cover and chill 8 - 12 hours.
Strain mixture through a fine mesh sieve into a pitcher. Serve with ice if desired, garnishing each serving with ground cinnamon or cinnamon sticks.