Combine the ground rice, blanched almonds, cinnamon and vanilla bean and seeds with 3 1/2 cups water and let sit overnight, covered, in the refrigerator.
The next day, strain the horchata using a strainer and cheesecloth. Press the solids against the cheesecloth-lined strainer to get out all of the liquid and serve over ice. (You could also blend the horchata, strain and serve over ice.)