Peel the beets and dice into approximately 1/2 inch cubes.
Combine the ingredients for the beet sour in a pot and simmer until the beets are softened. At that point, remove from heat, but do not discard the liquid.
Dice the onions.
Slice the carrots into rounds.
Slice the cabbage into long and thin strips.
Mince the garlic.
Melt the butter in a large pot.
Add the onions and a generous pinch of salt, then sauté until the onions start to soften.
Stir in the tomato paste, garlic, and seasonings.
Add the cabbage and carrots.
Add a little broth, to help the cabbage steam.
Cover until the cabbage has softened and cooked down a bit, stirring frequently.
With a slotted spoon, sieve, or other implement, move the beets from the brine to the soup.
Add the remaining broth.
If it's not sour enough, add a little bit of the brine at a time, to taste.
Top individual servings with sour cream and parsley.