Remove the beet greens and save for another recipe, and scrub beets well. Add to a small pot and cover with water, and bring to a boil. Reduce heat to a simmer and cook until the beets are tender and a knife slides right through (about 30-35 minutes). Save 2 cups of the cooking liquid, and allow to chill in fridge or freezer. Rub off and discard the skins of the beets, and chop into quarters.
Add all ingredients (except for garnish) to a high-powered blender, including 1.5 - 2 cups or so of the beet cooking water. Taste and adjust seasoning-- if it needs a little more brightness, add more vinegar, salt or lemon juice, but ours was perfect at this combination.
Refrigerate until very cold (ideally overnight.) Serve into small bowls, and add some minced fresh herbs* and a few droplets of oil and/or vinegar and some black pepper. Can also add seeds or nuts, avocado slices, feta or goat's cheese or minced onions as a garnish.
* speaking of herbs, go lightly. The flavor of this soup is really sweet and delicious, and a really powerful herb (like basil) can overwhelm it easily.