- Remove stems and leaves from beets, but leave on skins. In a deep pot, cover beets with cold water and bring to a boil. Boil until fork tender, about 40 minutes.
- Drain beets, but reserve two cups of the liquid. Strain the liquid and add to a large saucepan. Remove skin from beets. Grate beets through coarsest blade of grater. Add to beet liquid. Add beef broth, onion, salt, pepper and vinegar. Bring to a boil, and then cover and reduce heat to low. Simmer for 20 minutes, then remove from the heat.
- Chill in refrigerator for one hour, or until cold before serving. Ladle into bowls and top each serving with cucumber and a big spoonful of sour cream.