For the brown turkey stock: In a 4-quart saucepot over medium-high heat, brown the butter and add the giblets. Season with salt and pepper. Stir and cook until the giblets are browned. Add the carrots, celery and onions and cook, stirring, until the vegetables are browned. Add the turkey stock, rosemary, cinnamon, sage and star anise, bring to a boil and then lower to a simmer. Cook at a slow simmer until the stock is rich and dark and reduced to 5 cups, about 1 hour. Strain through a fine-mesh sieve and set aside.
For the gravy: When your turkey is done, measure out 1/4 cup of the fat from the roasting pan and discard the rest. Put the 1/4 cup turkey fat back into the roasting pan with the drippings, put the pan over medium-high heat and add a splash of the reserved 5 cups brown turkey stock to loosen the pieces. Whisk in the flour and remaining stock and simmer until the proper consistency is achieved, about 5 minutes. Add the heavy cream and vinegar and season to taste.