Using a sharp knife, peel the grapefruit, removing all of the bitter white pith. Working over a strainer set over a medium bowl, cut in between the grapefruit membranes to release the sections into the strainer. Squeeze the grapefruit juice from the membranes through the strainer. Reserve the juice and grapefruit sections separately.
Bring a small saucepan of water to a boil; fill a medium bowl with ice water. Blanch the watercress just until limp, about 30 seconds. Drain the watercress and cool it in the ice water. Drain the watercress again, squeezing out any excess liquid. Finely chop the watercress.
In a blender or food processor, puree the avocados with the blanched watercress, ginger, lime juice and the reserved grapefruit juice. With the machine on, add the chilled vegetable broth and ice water and puree the avocado soup until combined. Season the soup with salt and ladle it into bowls. Just before serving, garnish with the cucumber, chives and grapefruit sections and serve.
The avocado and grapefruit soup can be kept chilled for up to 3 hours.