Place your pot onto the stove-top. Add 2 tbsp Olive oil. Turn the heat to medium.
Chop half of your onion and add it to your pan.
Chop your cabbage and add that to the pot with the onions. Add 1 tsp of salt. Allow that to cook for 10-15 minutes. Stir occasionally to make sure nothing burns.
While those cook in your large pot, chop the rest of your onions, then your carrots, beets, and garlic.
In a separate pan, add the remainder of your oil and turn the heat to medium.
Add your onions first. Allow those to cook alone for 3 minutes. Then add your carrots and allow those to cook together for 5-6 minutes. Then add your beets and cook this altogether for another 6-8 minutes. Lastly, add your garlic and allow that to cook for another 1-2 minutes.
Add this onion, carrot, and beet mixture to your soup. Add another teaspoon of salt. Allow this to cook together while mixing for 3 minutes.
Add your broth to the large pot and turn your heat to high while mixing.
Chop your potatoes and add them to the soup mixture.
Add your tomato sauce, tomato paste, beans, and the rest of the seasonings to the mixture while mixing. Get the soup to a boil. Allow it to cook at a boil for about 20 minutes.
Add the vinegar to the soup. Allow that to cook for another 5 minutes.
Serve with a spoonful of sour cream and some dill on top. Enjoy!