Heat olive oil in a large pot over medium heat. Sauté onion, carrots, and garlic until soft, about 5-7 minutes.
Add grated beets, tomato paste, sugar, and vinegar to the pot. Cook for 5 minutes, stirring occasionally.
Pour in broth and bring to a boil over high heat.
Add chopped potatoes and cook until tender, approximately 15-20 minutes.
Stir in shredded cabbage and simmer for 10 minutes until cabbage is tender.
Season with salt, pepper, and fresh herbs to taste.
Serve hot with a dollop of sour cream and crusty bread.