Blend the beetroot with the shallots, stock and lemon juice in a blender or food processor. Add the sour cream or crème fraîche and blend once more. Season to taste. (Rinse out the blender or processor bowl immediately after use so that it doesn't stain.)
Chill in the refrigerator for at least 2 hours. Serve in small cups or individual bowls. Fresh mint makes a pretty garnish that contrasts well with the vivid red of the soup.