Prepare the stock: Melt 2 tablespoons butter in a large pot over medium heat. Add the turkey neck and giblets; cook, turning, until browned, about 3 minutes. Add the shallots, carrot, celery, thyme sprigs, bay leaf and broth. Reduce the heat to low and cook until slightly reduced, about 1 hour. Strain through a fine-mesh sieve into a large bowl; reserve the pot. You should have 7 cups stock?if you?re short, add more broth.
Pour the turkey pan drippings into a fat separator and let stand until the fat rises to the top. Discard the fat (or drizzle on your stuffing). Whisk the defatted drippings into the stock.
Melt the remaining 8 tablespoons butter in the reserved pot over medium heat. Add the flour and whisk until smooth and bubbling, about 2 minutes. Gradually whisk in the stock; bring to a simmer and cook, whisking occasionally, until thickened, 8 to 10 minutes. Season with salt and pepper.