In a large soup pot, heat olive or coconut oil. Add onion, ginger, and celery. Cook for about 5 minutes until soft.
Add turmeric and cook one more minute. Add squash, carrots, and broth. Bring to a boil, then reduce to a simmer and cook for 30 more minutes until the vegetables are soft.
Add the coconut milk.
Blend the soup with an immersion blender until the soup is smooth.
Season with salt and freshly ground pepper to taste, and serve.