Thinly slice the leek, use both the white and green parts. Put them on the bottom of your soup pot. Drizzle with a few tablespoons of extra virgin olive oil and sprinkle with salt. Cook on low flame for about 5 minutes, stirring often, until leeks are soft.
Add the cauliflower cut into florets, stir to mix with the leeks and cook for 5 more minutes to let the flavours mingle.
Cover with the hot water and cook on low flame until the cauliflower is so soft that you can mash it with a fork.
Add the beans and cook for about 5 minutes, then blend until smooth. Should it be too thick, add some more water.
Season with salt, a few turns of pepper and fresh thyme, then drizzle with fresh extra virgin olive oil and serve.