Heat olive oil in a large pot over medium heat. Add dill seeds, fennel seeds, and cumin seeds and cook for 1 minute, until fragrant.
Add onions and cook until softened, about 5 minutes. Add beets, cabbage, and beet greens and cook for another 5 minutes.
Stir in tomato paste, sugar, salt, and pepper. Pour in vegetable broth and bring to a boil. Reduce heat and simmer for 20-25 minutes, or until beets are tender.
Serve hot with a dollop of sour cream, a sprinkling of fresh dill, and slices of black rye bread.