Heat the olive oil in a large soup pot over medium. Add the chopped leeks and thyme. Stir and sauté the leeks until they are a bit soft, about 4 minutes. Add the chopped fennel and apples. Stir everything up a bit. Add the turmeric and stir to coat all of the vegetables evenly. Sauté the vegetables until the fennel is starting to soften, another 4 minutes. Add the walnuts and stir them in. Season the whole thing with salt and pepper. Add the vegetable stock and stir.

Cover the pot and bring to a boil. Simmer until all of the vegetables/apples are very soft, about 12-15 minutes. Remove the soup from the heat. Carefully blend the mixture in batches in an upright blender until totally smooth. Check the soup for seasoning and adjust accordingly.

Pour the puréed soup back into the pot. Bring the puréed fennel walnut soup to a boil and then serve hot with little drizzles of maple syrup, fresh black pepper, fennel fronds, and more toasted walnuts if you like.