Add beets and potatoes to the pot and cook for a few minutes.
Pour in beef broth, add tomato paste, vinegar, and sugar. Bring to a boil, then reduce heat and simmer for 45-60 minutes, or until vegetables are tender.
Stir in baked beans and season with salt and pepper to taste.
Serve hot with a dollop of sour cream or Greek yogurt and a sprinkle of dill.