Brown the beef and cook the onions, then simmer - Add a bit of olive oil to a stockpot. Brown the beef on all sides, then add the chopped onions to the pot. Cook until the onions are soft. Add 4 cups of broth and bring to a boil. Lower the heat to a simmer, cover, and cook until the meat is spoon tender, about an hour and a half.
Meanwhile, prep and roast the root veg - Preheat the oven to 400 degrees. Peel and chop the beets, carrots, and potatoes into 1/2 inch pieces. Toss the beets and carrots with olive oil and spread them out in a single layer on a lined baking sheet. Roast for 15 minutes. Toss the potatoes with olive oil and add them to the pan, roasting everything for an additional 15 minutes.
Slice the cabbage - While the beef is simmering and the veg is roasting, thinly slice the cabbage and set aside.
Assemble and cook the soup -Add the remaining broth, the roasted carrots, beets, and potatoes, sliced cabbage, and a half cup of the fresh dill to the pot. Bring to a simmer, and cook until the cabbage is cooked through and has taken on the hue of the beets.
Finish and Serve - Add 3 T vinegar and season to taste with salt and freshly ground black pepper. Serve with a dollop of sour cream and a a handful of fresh dill.
Notes
I recommend serving this with a salad of butter lettuce, supremed oranges, thinly sliced red onion, oil cured black olives, and white balsamic vinaigrette.