To make this soup, start by preparing the leeks. Wash the leeks and slice them on the diagonal to cut them in half, reserving only the whites and light greens for the soup.
Next, heat a large pot or dutch oven on the stove, over medium heat. Add in the butter (or olive oil, if using).
Once the butter is hot and melted, add the sliced leeks in and sauté them for about 5 minutes.
Then, add in the onion, garlic, and seasonings (kosher salt, ground black pepper, and thyme) and sauté them together with the leeks for another 4-5 minutes.
Once the onions have softened, add in the potatoes, the broth, and the heavy cream (or coconut milk or non-dairy milk) and stir.
Bring the soup to a gentle boil. Then, once the soup is boiling, cover the pot and turn the heat down to low, allowing the soup to simmer for 20 minutes, until the potatoes are tender.
Then, remove the soup from the heat and use an immersion blender to blend the soup, leaving just a little bit of texture. Make sure to not over-blend the soup - this is important!
Once the soup is done, transfer it into bowls and garnish it with chopped chives, olive oil, a drizzle of cream, and a pinch of sea salt and black pepper. Then, serve and enjoy!