For the beets, peel them and trim off both ends. Dice 2 beets and shred 1 beet, keeping the chopped beet separate from the shredded beet (because they get added at different times).
Heat the oil over medium heat in a 5-quart pot. Once hot, add the onion and garlic and cook until fragrant, about 5 minutes, stirring frequently.
Add the stock and cabbage and bring it up to a boil. Cover the pot and turn the heat down slightly so it doesn’t boil over, and cook 10 minutes.
Add the diced beet. Bring back up to a boil, cover the pot, and turn the heat down slightly so it doesn’t boil over, and cook 10 minutes.
Add the shredded beet, carrot, celery, potato, tomato paste, salt, black pepper, and allspice. Bring back up to a boil, cover the pot, and turn the heat down slightly so it doesn’t boil over, and cook until the vegetables are tender, about 30 minutes.
Remove from the heat and stir in the lemon juice and dill.
Taste and add additional salt and lemon juice if desired.
Serve along with fresh lemon wedges and more dill on top.