For a lighter version of this soup, use half & half instead of the cream. Slideshow: More Turkey Soup Recipes
In a large heavy pot, heat the butter over medium high heat until hot. Season the turkey with 1/2 teaspoon salt and 1/4 teaspoon pepper, then brown, in batches if necessary, about 6 minutes per batch. Sprinkle the flour over the bottom of the pot and cook, stirring, until fragrant and nutty, about 4 minutes.
Stir the onions, celery, and 1/4 teaspoon each salt and pepper into the pot and cook, stirring occasionally, until golden, about 6 minutes. Stir in the stock and bring to a gentle boil. Cook until the turkey is very tender, about 1 1/4 hours. Transfer the turkey to a plate and cool to warm, then shred the turkey, discarding the bones and return the meat to the pot. Stir in the cream and season with salt and pepper to taste. Serve garnished with the parsley.