Slice the leeks, making sure to wash them thoroughly to remove any grit. Peel and chop the parsnips into uniform pieces.
Heat 2 tablespoons of olive oil in a large pot over medium heat. Add the sliced leeks and sauté for about 5-7 minutes until they become soft and translucent. Add the chopped parsnips and continue to cook for another 5 minutes, stirring occasionally.
Pour in the 4 cups of bone broth (or vegetable broth) and bring the mixture to a boil. Reduce the heat and let it simmer for 15-20 minutes, or until the parsnips are tender.
Using an immersion blender, blend the soup until smooth and creamy. Alternatively, carefully transfer the soup in batches to a countertop blender.
Stir in the coconut milk and add fresh thyme leaves, garlic powder, and ground white pepper. Taste the soup and adjust seasoning with sea salt as needed.
Allow the soup to simmer for an additional 5 minutes to let the flavors meld. Serve hot, garnished with extra fresh thyme if desired.