Special equipment: a spice grinder, a sieve and some cheesecloth
Grind the rice to a fine powder in a spice grinder; transfer it to a large bowl. Coarsely grind the almonds in the grinder; transfer them to the bowl. Add the cinnamon and lime peel if using to the bowl, pour in 2 cups warm water and give the mixture a quick stir. Cover, and refrigerate for 8 hours. (Don't shortcut this first step in achieving horchata milkiness; it takes time for the starch in the rice to seep into the water.)
Line a sieve with a double or triple layer of cheesecloth, depending on how fine your sieve is, and set the sieve over a large pot or bowl; set aside.
Remove the cinnamon and lime peel from the rice-almond mixture; transfer the rest (liquids and solids) to a blender. Add the sugar and salt, and blend until the mixture is as smooth as you can get it, with minimal grit; the timing will depend on the strength of your blender. (Again, no shortcuts here: Blending until smooth creates the thickness and body of the horchata.)
Pour this mixture through the lined sieve in small batches, giving each enough time to drip through. (As the rice-almond mash builds up in the cheesecloth, subsequent batches will take longer to strain.) Once all the liquid has passed through, gather up the cheesecloth and give it a tender squeeze (don't wring it out). Add 4 cups cold water to the strained liquid. Cover and refrigerate until chilled, at least 2 hours and up to 5 days.
Before serving, give the horchata a good stir (even if you were patient with straining, there will still be some solids), then serve it in glasses over ice.
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