Using a fork, scrape the sides of the cooked squash into spaghetti-like strands. Spray slow cooker with cooking spray. Add spaghetti squash strands, cooked turkey, onion, mushrooms, garlic, salt, and pepper to the slow cooker. Stir to mix well.
In a medium saucepan, melt butter over medium heat. Whisk in broth, heavy cream, and xantham gum (if using). Turn off heat and stir in cheese. Whisk until cheese is melted.
Pour sauce over the food in the slow cooker. Top with Parmesan cheese.