Soak the almonds and rice in plenty of water for 12 to 24 hours. Drain and rinse, and transfer them to a blender. Add 5 cups water, and blend on the highest speed until smooth.
Line a medium strainer with several layers of cheesecloth or a thin kitchen towel, and place it over a medium bowl. Pour the mixture through the strainer, gather the corners of the cloth and gently squeeze out all the liquid; discard the pulp.
Return the liquid to the blender, add the maple syrup and vanilla and blend until combined. Pour the horchata into a jar, and refrigerate for up to 5 days. Serve chilled.
Recipe courtesy of Amy Chaplin