To make the soup, wash the cauliflower, discard the leaves, and cut the cauliflower into florets.
Peel the potatoes, the sweet potato, and the onion. Chop everything.
Bring the water to a boil, add the vegetables, and let simmer on low to medium heat until everything is cooked through. Add salt and pepper and puree the soup using an immersion blender. Once the soup is nice and creamy, taste test it and adjust the seasoning to your taste.
To make the pesto, mince the parsley and mix in the remaining pesto ingredients.
Serve the soup with tiny heaps of pesto sprinkled on top.