Heat a large saucepan over medium heat. Add the bacon and cook until crisp. Remove from pan and add the olive oil.
Add the leeks and celery and cook until softened. Add the garlic and cook for about a minute. Stir in the parsnips and add the broth. Bring to a boil and reduce to a simmer.
Simmer until parsnips are softened, about 10-15 minutes. Transfer to a blender and blend until smooth. Transfer back to pan and stir in the coconut milk, nutmeg and reserved bacon. Season to taste with salt and pepper and simmer over low heat until heated through.