In a large saucepan, cover the beets with cold water by l inch. Stir in 1/4 cup of the vinegar and 2 tablespoons salt. Bring to a boil, lower the heat, and simmer, covered, until very tender, about 30 minutes. Drain, cool, and peel the beets. Dice the beets and set aside.
Heat the butter in a large pot over medium heat. Add the celery, leeks, garlic, and caraway seeds and cook, covered, stirring occasionally, until soft, about 8 minutes. Add the cabbage and cook, stirring, until wilted, about 3 minutes.
Tie the parsley sprigs, thyme, and bay leaf together with a piece of kitchen twine and add to the pot with the beets, tomatoes, and broth. Bring to a boil, lower the heat, and simmer, covered, for 10 minutes to bring the flavors together.
Stir in the remaining 3 tablespoons vinegar and the remaining 2 teaspoons salt. Season with pepper to taste. To serve divide among warm soup bowls, top with dollops of the sour cream and sprinkle with the dill. Serve with additional vinegar at the table.
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