Prep the Leeks: Cut the root ends and dark green parts off of the leeks, leaving only the tender white and light green parts. Cut each leek in half lengthwise, then run under water until clean, making sure to check the outer few layers of the leek for hidden dirt. Chop into ¼” pieces. Prepare the remaining ingredients, if you haven’t already
Sauté Aromatics: Melt the butter in a dutch oven or large pot over medium heat. Add the chopped leeks along with a pinch of salt and pepper. Sauté for 6 to 8 minutes, until the leeks are translucent and their volume has reduced by half. Add the celery, garlic, thyme, bay leaves, and additional salt and pepper (I used ½ teaspoon of each) to the pot and sauté for an additional 2 minutes, until the garlic is fragrant.
Simmer: Add the potatoes, broth, coconut milk, and water to the pot and stir well. Increase the heat to high and bring to a boil. Then, reduce the heat to medium and maintain a simmer for 15-20 minutes, or until the potatoes are fork-tender.
Blend: Use an immersion blender to blend the soup until smooth, or carefully transfer the soup to a blender with a venting lid and blend until smooth. I prefer my soup to be smooth, but you can leave a portion of it unblended for a chunkier texture, if you wish. Season with additional salt and pepper to taste if necessary. If the soup is too thick for your liking, thin it out with more water or broth.
Serve: Serve warm, topped with chopped chives, parsley, celery leaves, or croutons. Leftovers will keep in the refrigerator for up to 5 days, or can be stored in the freezer in jars or airtight containers for up to 2 months.