Heat the oil in a 5-quart pot over medium-high heat; once hot, add the meat in a single layer and cook until browned on both sides, about 4 minutes, flipping once. (You might need to do this in 2 batches so you don’t overcrowd the pan.)
Add the bay leaf and 4 cups (.95 L) beef broth, and bring to a boil. Cover the pot, turn heat down to simmer, and cook 1 hour, stirring occasionally.
While the beef cooks, chop all the vegetables. For the beets, shred ⅓ of the beets and finely chop the remaining ⅔. Add the finely chopped beet to the pot; bring back up to a boil, then cover the pot and cook 10 minutes.
Add the shredded beet, carrot, celery, onion, potato, cabbage, garlic, salt, black pepper, allspice, tomato paste, and remaining 4 cups beef broth. (The vegetables should be just covered with liquid; you can add water if you need more liquid to cover them.) Cover the pot and bring it back up to a boil, then turn the heat down to simmer and cook until the vegetables are tender, about 30 minutes.
Add the vinegar, then turn off the heat and stir in the dill. Taste and add additional salt and pepper as desired.
To serve, ladle the soup into bowls; top with a dollop of sour cream and a sprinkling of fresh dill.