Add the cauliflower, salt to taste, and 1/2 cup water. Raise the heat slightly, cover the pot tightly and stew the cauliflower for 15 to 18 minutes, or until tender. Then add another 4 1/2 cups hot water, bring to a low simmer and cook an additional 20 minutes uncovered.
ASK THE HOTLINE ABOUT THIS STEP!
Working in batches, purée the soup in a blender to a very smooth, creamy consistency. Let the soup stand for 20 minutes. In this time it will thicken slightly.
Thin the soup with 1/2 cup hot water. Reheat the soup. Serve hot, drizzled with a thin stream of extra-virgin olive oil and freshly ground black pepper.