Add onions. Heat 2 teaspoons oil in a large, thick-bottomed pot on medium high heat. Let onions slight caramelize
Peel and chop the beets, carrots, and potatoes into 1/2-inch pieces. Toss the beets and carrots with a teaspoon or two of olive oil and spread them out in a single layer on a foil-lined roasting pan. Roast in a 400°F oven for 15 minutes.
Toss the potatoes with olive oil and make room for them in the roasting pan, and roast everything an additional 15 minutes.
Return the pot to the stove and add the remaining broth, the carrots, beets, and the diced potato. Add the chopped meat to the pot, the sliced cabbage, and a half cup of the fresh dill. Bring to a simmer, and cook for another 15 minutes or so, until the cabbage is cooked through.
Add the vinegar and season to taste with salt and freshly ground black pepper. I use about 2 teaspoons of salt and 1 teaspoon of pepper, but the amount you use will depend on how salty your veg broth is to begin with.
Serve ladled into bowls with a dollop of sour cream and a sprinkling of fresh dill.
NOTE: The soup is best made a day ahead, giving the flavors time to meld. The longer the soup sits, the more it will all turn the deep red color of beets.