It's made with chufas - tiger nuts - which are tiny tubers, gluten and cholesterol free, and sold in health food shops (fishing enthusiasts use them to catch carp and some hunters attract wild turkey with them). They are extremely nutritious.
The drawback is that - as with lots of traditional Spanish food - horchata is generally served with plenty of sugar
250gms tiger nuts
1.25 litres water
stick cinnamon, strip of unwaxed lemon peel
Wash the tiger nuts as thoroughly as possible. Leave to soak in cold water for 12-15 hours (change the water periodically if you can)
Wash the tiger nuts again and make sure that no traces of dirt remain (water should rinse clear)
Put the tiger nuts and a portion of the 1.25 litres of water in a blender/liquidiser/food processer and whizz until the tiger nuts become a pulp (without water, this can be done with a pestle and mortar if you have the patience).
Combine the wet pulp with the rest of the water and the lemon rind and cinammon and leave the mixture somewhere cool for 2 hours (a fridge is fine).
Sieve the mixture (ideally through muslin), add and dissolve sugar to taste (200/250gms sugar is a guide - experiment to find your own preference) and leave it to cool. Should have the same consistency of soy milk.
If you can’t drink it the same day, freeze what you have left, just don’t keep it in the fridge for too long.
Can be drunk as is or frozen and drunk as slush/granita. It's often mixed in Spain with strong iced coffee.
I've been advised by one of Alicante's best horchaterias (Heladeria Gori) not to use a straw to drink liquid horchata as this will prevent you from appreciating many of the complex flavours.
The main problem with tiger nuts is getting them fresh enough, they aren't so good after a year of storage. They should also be kept well ventilated somewhere cool and dark - they can harbour mold and bacteria if kept in a plastic bag.
It's worth searching out properly made horchata in Spain - many cafes will sell commercially produced liquid which is quite vile. And even the quality from horchaterias can vary - if you can detect a chemical taste it could be because the chufas were cleaned with some kind of bleach. I understand Gori's chufa's go through a special pasteurisation process.
A reputable wholefood store shouldn't sell you chemically washed tigernuts - if you clean them properly I would expect no problems. However, my advice would be not to give horchata to the very young or those with weakened immune systems without medical approval.