In a large pot, bring the broth to a boil. Add the beef or pork and cook for about 1-1.5 hours, or until the meat is tender.
Remove the meat from the pot, shred it or cut it into bite-sized pieces, and set aside. Discard the bones if used.
In a separate skillet, heat the vegetable oil over medium heat. Add the chopped onion and grated carrot. Sauté until the vegetables are soft and golden brown, about 5-7 minutes.
Stir in the tomato paste and cook for an additional 2 minutes.
Add the diced potato to the pot with the broth. Cook for about 10 minutes, or until the potatoes are tender.
Add the sauerkraut, shredded cabbage, sautéed vegetables, garlic, bay leaf, and dill to the pot. Stir well.
Return the shredded or diced meat to the pot. Simmer the soup for another 15-20 minutes, allowing the flavors to meld together.
Season the soup with salt and black pepper to taste. If desired, add vinegar and sugar to adjust the flavor. Stir well and taste, adjusting as necessary.
Remove the bay leaf before serving.
Enjoy your meal!