Peel beets and cut into cubes. Rinse sorrel, set 4 leaves aside and tear the rest. Rinse fennel. Chop the greens and set aside. Chop the bulb into small pieces.
Cook all vegetables until tender in the vegetable broth, about 40 minutes. Pour through a sieve to collect juice. Serve warm or cold, garnished with sorrel and fennel greens.