Combine almonds and rice in a blender. Add boiling water and let sit 15 minutes.
Cover loosely with a paper towel and blend on high 1 minute, or until smooth. Strain into a pitcher and stir in rice milk. Chill until cold.
To serve, place bottles of syrup, horchata, glasses, ice, rum (if using), and cinnamon sticks on the bar.
Let your guests make their own horchata flavor by filling a glass with ice, filling with horchata, and adding a shot (about 1 tablespoon) of syrup and a shot of rum (for adults), stir to combine with a cinnamon stick.