In a large soup pot over medium high heat, sauté the oil, onion, garlic, and kielbasa for 5 minutes until the onion is soft.
Add the water, vinegar, brown sugar, and black pepper, stirring to mix well.
Stir in the cabbage, potatoes, and carrots.
Bring it to a boil over high heat, then reduce the heat to medium low, cover, and simmer for about 15 minutes or until vegetables are tender.