In a large saucepan, cover the beets with water. Bring to a boil and cook over moderately high heat until tender, about 1 hour; if necessary, add more water to keep the beets covered. Drain the beets and let cool slightly, then peel and coarsely chop.
Wipe out the saucepan and heat the olive oil in it. Add the shallots and cook over moderate heat until softened, about 4 minutes. Add the tomatoes and chopped beets, season with salt and pepper and cook, stirring occasionally, until the tomatoes release their juices, about 5 minutes. Add the 1 teaspoon of cumin and cook, stirring, until fragrant, about 1 minute. Stir in the vegetable stock and tomato paste and bring to a boil. Cover and simmer over low heat for 10 minutes.
Puree the soup in batches in a food processor. Rewarm the soup in the saucepan and season with salt and pepper.
Ladle the soup into bowls and top with dollops of crème fraîche. Sprinkle with a little cumin and the parsley and serve.