Heat the oil in a large saucepan over medium heat. Add the sliced leeks, garlic, celery, half the thyme leaves and some salt and pepper. When the veg is sizzling nicely, cover the pan, reduce the heat, and let them sweat for about 10 minutes, until the leeks are fairly soft stirring from time to time.
Meanwhile, prepare the cauliflower: trim off any thick outer leaves and the base of the stem if it looks coarse and grubby, then roughly chop the cauliflower - stalk and all.
Add the chopped cauliflower to the softened leeks and stir well then pour the vegetable stock. Bring to a simmer, cover, and cook for 5-10 minutes, until the cauliflower is tender, but not mushy.
Remove the pan from heat. Add the mustard, mix well. Puree the soup using a blender or a hand blender. You may need to do it in two batches.
Add a splash of water if it's too thick.
Ladle the soup into bowls, trickle some oil if you like, and sprinkle the rest of the thyme and some pepper. Enjoy!
Notes
This soup will last for up to 3 days in the fridge. You can easily sub the leeks for 3 white onions if you like!