Add coconut oil to a saucepan over medium heat. Add the leeks, celery, and salt, and sauté until translucent, about 5 minutes.
Add in the carrots, apple, ginger, and cardamom and stir until well coated. Pour in the broth and bring to a boil. Then turn heat to low, cover, and simmer for about 30 minutes or until carrots are tender. Stir in the coconut milk and simmer for an additional two minutes.
Transfer the soup to a blender and process until smooth or purée the soup directly in the pot with an immersion blender. Season with salt and pepper, add a drizzle of of coconut milk, and garnish with cilantro.