Place the rice, almonds and cinnamon stick in 3 cups of water in a glass bowl. Cover with a cloth and soak for 6 to 8 hours or overnight.
Pour rice mix into a blend and puree until smooth. Strain into a pitcher using a fine mesh or cheese cloth. You might need to strain a couple of times to remove the majority of the solids from the horchata.
Stir in the milks, vanilla and remaining cup of water. Taste and adjust to taste with more sugar and water if needed.
Chill until cold and serve as is or over ice.
Notes
*If you don't like almonds or have a nut allergy, leave out the almonds.