In a Dutch oven or heavy pot, heat olive oil over medium-low heat. Add the leeks, season with salt, and cook until the leeks are wilted and transparent, about 5 to 7 minutes. Reserve 1/4 cup of the leeks for garnish and leave the rest in the pot.
Add the potatoes, cauliflower, and vegetable stock. Bring to a boil, then lower heat to a simmer. Cook until the potatoes are fork tender.
Working in batches, puree the soup in a blender. Return soup to the pot and season to taste with salt and pepper. An immersion blender makes this even easier, if you have one. Add a little more stock if the soup is too thick.
Serve the soup hot and garnished with reserved leeks and a drizzle of olive oil, if desired.
Cauliflower and Potato Soup Tips
How to Clean Leeks: Clean the leeks by letting placing chopped leeks in a large bowl of cold water. Swirl the leeks and let it sit for 5 minutes to let the dirt settle to the bottom. Use your hands or slotted spoon to transfer leeks to a clean kitchen towel or paper towels.
Can I use other soup stock? Yes! I've used clam stock and chicken broth - they work beautifully, but of course, only if you don't mind the soup not being vegetarian.
My soup seems too thick. Simple blend in more soup stock if you want a thinner soup.