In a large saucepan over medium-high, heat the oil. Add the onion and cook until just starting to brown, 3 to 5 minutes. Add the sausage and cook, breaking it up, until lightly browned, 3 to 5 minutes. Add the fennel and dill seeds and cook for another 30 seconds. Add the stock and bring to a simmer.
While the stock heats, fit a food processor with the large grating attachment. Grate the beets. Add the beets and any liquid in the processor to the pan. Bring to a simmer and cook for 5 minutes. Season with salt and pepper. Ladle into bowls and serve topped with sour cream and dill. Makes 6 servings.