Heat olive oil in a large pot over medium heat. Add onion and garlic, sauté until soft.
Add beets and carrots, cook for 5 minutes.
Stir in tomato paste and cook for another 2 minutes.
Add potatoes, cabbage, diced tomatoes, and vegetable broth. Bring to a boil.
Reduce heat, cover, and simmer for 45 minutes.
Stir in sugar, vinegar, salt, and pepper. Cook for another 5 minutes.
Serve hot, garnished with fresh dill.