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Cut kielbasa in half lengthwise, then crosswise into 1/4-inch-thick slices. Cook in a large pot over medium-high heat, stirring, until browned and the fat has rendered, about 5 minutes. Transfer to a plate with a slotted spoon.
Add oil, onion, carrot and celery to the pot and cook, stirring often, until starting to brown, about 5 minutes. Reduce heat to medium and continue cooking, stirring often, until the vegetables are soft, about 4 minutes more. Add garlic and cook, stirring, for 1 minute. Add cabbage and cook, stirring occasionally, until slightly wilted, about 3 minutes.
Add broth, potatoes, dill, caraway, paprika, pepper and salt. Cover and bring to a boil. Reduce heat to maintain a simmer and cook, uncovered, until the potatoes are tender, about 30 minutes. Stir in vinegar and the kielbasa. Serve topped with sauerkraut and/or sour cream, if desired.