Melt the butter in a heavy saucepan or Dutch oven over medium heat. Add the celery and onion to the pot and cook until translucent, about 5-8 minutes.
Stir in the flour and cook for about 3-5 minutes, until light brown in color. Add stock gradually, stirring continually, until combined and no lumps of flour remain.
Bring mixture to a boil, then reduce heat to simmer. Cook until slightly thickened and smooth.
Stir in shredded carrot and cook until carrot is tender, approximately 2 minutes.
Stir in wild rice, chopped turkey, potatoes, and wild mushrooms, if using, and cook until ingredients are heated through, approximately 5 minutes. Stir in cream and bring mixture almost to a boil (do NOT boil once cream has been added).
Season soup with salt and pepper to taste. Garnish with additional small wild mushrooms and fresh chopped parsley and freshly ground black pepper, as desired