Combine rice and cinnamon stick in a blender with water. Blend for about 2 minutes. Rice mixture will be coarse. Transfer rice mixture into a bowl and refrigerate for about 1 hour. Strain mixture through a fine mesh strainer into a pitcher. Add agave nectar and stir. Add milk to rice mixture and refrigerate for 1 more hour.
Add ice cubes to a glass. Add 2 shots of espresso and pour horchata enough to fill the glass. Garnish with a cinnamon stick and enjoy.