Prepare Leeks: First, cut off and discard (or save for broth) the end and the darker green parts of the leek. Cut the remaining white and light green parts in half lengthwise, and wash under cold running water, making sure to clean between the layers. Slice these cleaned parts into 1/4-inch thick pieces.
Cook Leeks and Celery: Heat the olive oil in a large pot or Dutch oven over a medium setting. Add your sliced leeks and celery to the pot, cooking until they become slightly tender and emit a pleasant aroma, approximately 5 minutes. Following this, incorporate the sea salt, black pepper, dried thyme, and minced garlic, and cook for another minute or two, ensuring to stir well.
Add Potatoes: Next, introduce the potatoes to the pot, stirring them into the leek and celery mixture. Continue to sauté this mixture for about 3-4 minutes, making sure the potatoes are well-coated and begin to absorb the flavors.
Simmer with Liquids: Pour in both the water and the light coconut milk, bringing the mixture to a boil. After reaching a boil, reduce the heat to a simmer, cover the pot, and allow it to cook for 20-25 minutes. Stir the mixture occasionally, ensuring the potatoes become soft yet remain mostly intact.
Blend for Texture: Using an immersion blender, blend about three-quarters of the soup directly in the pot, leaving chunks of potatoes for a varied texture. Alternatively, you can blend half of the soup in a blender until smooth and then reintegrate it into the pot. Adjust the consistency according to your preference.
Adjust Seasonings: Taste the soup and make any necessary adjustments to the seasoning with additional salt, pepper, or thyme to enhance its flavor.
Serve and Garnish: Serve the hot soup in bowls, and if desired, garnish with green onions, coconut bacon, and vegan sour cream for added taste and presentation.