In a large pot, heat the olive oil over medium heat. Add the onion, celery, and carrot, stirring occasionally. Cook until somewhat softened and onion is starting to become translucent, about 15 minutes.
Add garlic, stirring frequently, and cook for 2 more minutes. Add the apple cider vinegar and scrape up any browned bits on the bottom of the pot.
Add the butternut squash, applesauce, cinnamon, ginger and nutmeg. Cook for 2 minutes. Add the chicken stock, heavy cream, salt, pepper, and cajun seasoning. Bring to a boil, then reduce down to a simmer. Cover the pot and simmer for 1 hour, or until squash and carrots easily fall apart when cut with the side of a spoon.
Use an immersion blender or transfer to a stand blender and blend until completely smooth. Serve hot with garnishes (optional).
