Clean the leeks: Trim the root ends and dark green parts, slice lengthwise, and rinse thoroughly under running water and then in a large bowl of water. This is a really important step. It is super important to wash the leeks properly. They are known to hide bits of sand in the stalks, and then you get a sandy soup 😜.
Pat dry with a kitchen towel, then slice thinly into half-moons.
Slice the shallot.
In a Dutch oven or large soup pot, heat butter and heat oil over medium heat and add the sliced leeks and shallot with a pinch of salt. Cook gently for 5–7 minutes, stirring occasionally, until soft and translucent but not browned.
Stir in the minced garlic and fresh thyme, and cook for 1 more minute until fragrant.
Add the white wine if using. Let it simmer for 2 minutes to cook off the alcohol.
Add the cauliflower florets and diced potatoes, stirring well to coat with the aromatic mixture.
Pour in the water (or vegetable broth or chicken stock if you really want to), and add the bay leaf and pinch of nutmeg if using. Bring to a gentle boil, then reduce to medium-low heat, cover, and simmer for about 20 minutes or until vegetables are tender when pierced with a knife.
Remove the bay leaf, then carefully blend the hot soup using an immersion blender, regular blender, or food processor until the soup is silky and smooth. (For the finest texture, strain through a fine-mesh sieve or chinois strainer.)
Return to the stove on low heat. Add more water if you would like a thinner soup. Do not boil.
Ladle into warm bowls. Serve with a quenelle (spoonful) of crème fraîche or heavy or vegan cream, and season with black pepper, a pinch of nutmeg, and more salt to taste.
Garnish with green onions or chives, a little parsley or chervil leaves, or a drizzle of olive oil.