How to Make It
In a medium saucepan, heat the 2 tablespoons of lemon olive oil. Add the sliced fennel and a pinch of salt, cover and cook over moderately low heat, stirring a few times, until the fennel is softened, about 10 minutes. Add the water and bring to a boil. Simmer over low heat until the fennel is very tender, about 20 minutes.
Working in batches, puree the fennel soup in a blender until smooth. Transfer the soup to a medium bowl and refrigerate until chilled, about 1 hour.
Stir the grapefruit juice into the fennel soup. Add the sugar to the soup and season with salt. Ladle the soup into bowls, garnish with a little lemon olive oil and chopped fennel fronds and serve.
Olive oil pressed or infused with lemon is available at most supermarkets and specialty food stores.