Peel and finely dice onions and garlic. Clean the cabbage, quarter it, cut out the stalk. Wash the cabbage, drain and cut into strips.
Heat oil in a pan. Fry the mince in it until crumbly. Season with salt and pepper and remove. Fry the cabbage, onions and garlic in the frying fat, turning for about 2 minutes. Stir in tomato paste, sauté briefly. Add the mince again and season everything with salt, pepper, paprika and sugar. Deglaze with the broth and tomato juice. Bring to the boil and stew covered for approx. 15 minutes.
Wash and finely chop the dill. Possibly season the braised cabbage again and serve with crème frâiche. Sprinkle the dill on top.