Step 1In a non-reactive pot or container, combine the buckwheat, water, cardamom, cloves and cinnamon stick. Cover and steep the mixture for 2 hours on the countertop, or refrigerate overnight.
Step 2Pour the mixture into a blender (this may need to be done in batches, and add additional water if needed to thin if the buckwheat has absorbed all of it) along with the honey and salt and blend at high speed until the buckwheat is completely broken down, 4 to 5 minutes. The mixture will look like brown sand with cloudy white water floating above it.
Step 3Strain the mixture using a fine mesh strainer, pushing out all of the liquid and discarding the solids. Add additional water to thin if desired. This makes about 2 quarts horchata, depending on your desired thickness. The horchata will keep, covered and refrigerated, up to 3 days. Serve over ice.