In a large soup pot, over medium high heat, sauté leeks in olive oil, until the leeks are soft and fragrant.
Add the remaining ingredients, all except the coconut milk, to the soup pot and bring to a boil. Use just enough liquid to almost cover the vegetables – adjust as necessary. You can always add more later to the pureed soup to get the consistency you like.
Reduce heat to a simmer and cook the vegetables until vegetables are tender - 20-30 minutes. Puree the soup in batches in a high-speed blender, return to the pot, add the coconut milk and heat through. Taste for seasonings and serve. Serves 6-8.