Place a rack in the bottom third of the oven. Preheat oven to 350°F.
Prepare the Mushroom-Flavored Forcemeat. (See separate recipe.).
Stuff the turkey with forcemeat and truss with kitchen string. Spread the softened butter evenly over the turkey. Season with salt, pepper and paprika. Bake any leftover stuffing in a small casserole, just like meat loaf.
Spread the carrots, celery, and onion the bottom of a flameproof roasting pan large enough to hold the turkey. Place the turkey on top of the vegetables. Add the neck and giblets and pour the reserved soaking liquid from the porcini mushrooms (see Forcemeat recipe) into the pan.
Roast the turkey for 1 hour. Reduce the heat to 300°F and roast until cooked through, 2-1/2 hours or more for a 12–14 pound turkey. An instant-read thermometer should register between 160 to 180°F when thrust into the thickest part of the thigh without touching the bone. Baste the turkey every 15 minutes the entire time that it is roasting. Baste with drippings, alternating with the melted butter. If necessary, add 1 cup water or chicken broth to the drippings in the bottom of the pan. If the turkey starts to get too brown, cover loosely with aluminum foil. Remove the foil for the last 20 minutes to crisp the skin.
Remove the turkey from the over to a platter. Let rest for 30 minutes before carving.
While the turkey is resting, prepare the gravy: Place the roasting pan over high heat. Add the cognac and port and bring to a boil while stirring with a wooden spoon to scrape up the little browned bits on the bottom of the pan. Add a little water if the gravy seems too dry. Remove from the heat and strain out all the vegetables. Pour the liquid into a degreasing cup (also called a gravy separator). Let stand for a few minutes to let the fat rise to the top, then pour out the pan juices at the bottom of the cup into a saucepan. (All the fat will be left behind.) Reheat and serve as pan juices with the turkey. If you prefer a thicker gravy, whisk the buerre manié into the juices and, stirring constantly, boil until the gravy is smooth and thick, about 2 minutes.
Untie the turkey and carve it as you would a chicken. Scoop out the forcemeat and serve it on the side.