At least 2 hours before roasting the turkey, chop the turkey neck into J-inch pieces. Heat the oil in a medium saucepan over medium heat. Add the neck, turkey heart, and gizzard. Cook, stirring occasionally, until the turkey pieces are well browned, about 10 minutes. Add the stock, bring to a simmer over medium-high heat, scraping up the browned bits in the pan. Reduce the heat to very low and simmer for 2 hours. Strain the stock and set aside. Let stand 5 minutes and skim off any fat that rises to the surface. You should have 1½ quarts stock; add water to the stock, if needed. (The stock can be prepared up to 1 day ahead, cooled, covered, and refrigerated.) Set aside.

Position a rack in the lower third of the oven and preheat the oven to 325°F. Turn the turkey on its breast. Loosely fill the neck cavity with stuffing. Using a thin wooden or metal skewer, pin the turkey’s neck skin to the back. Fold the turkey’s wings akimbo behind the back or tie to the body with kitchen string. Loosely fill the large body cavity with some of the stuffing, and cover the stuffing with foil. Place any remaining stuffing in a lightly buttered casserole, cover, and refrigerate to bake as a side dish. Tie the drumsticks together with kitchen string.

Place the turkey, breast side up, on a rack in the roasting pan. Rub all over with the 4 tablespoons softened butter. Season with ½ teaspoon salt and ¼ teaspoon pepper. Tightly cover the breast area with aluminum foil. Pour 2 cups stock into the bottom of the pan.

Roast the turkey, basting all over every 40 minutes with the juices on the bottom of the pan (lift up the foil to reach the breast area), until a meat thermometer inserted in the meaty part of the thigh (but not touching a bone) reads 170°F and the stuffing is at least 160°F, about 3 hours. Whenever the drippings evaporate, add water to moisten them (about 1½ cups at a time). During the last 45 minutes, remove the foil and baste a couple of times to brown the skin.

Transfer the turkey to a large serving platter and let it stand for at least 20 minutes before carving. Increase the oven temperature to 350°F. Cover and bake the stuffing until heated through, about 20 minutes.

Meanwhile, pour the drippings from the roasting pan into a separator cup. Let stand 5 minutes; then pour off and reserve the drippings and discard the fat. Return the drippings with the remaining 1 quart stock to the roasting pan. Place the roasting pan over two burners on high heat, and bring the stock to a boil, scraping up the browned bits on the bottom of the pan with a wooden spatula. Boil until the liquid is reduced to 2 cups, 10 to 15 minutes.

In a small bowl, sprinkle the cornstarch into the port and stir to dissolve. Stir into the pan and cook until the sauce is lightly thickened. Remove from the heat. One tablespoon at a time, whisk in the remaining 2 tablespoons butter until melted. Season with salt and pepper. Strain the sauce and pour into a warmed sauceboat.

Carve the turkey and serve with the stuffing and gravy. If the dark meat seems a bit pink, do not be concerned, because it is safe to eat. If you want it cooked longer for aesthetic reasons, cut the thighs and drumsticks from the carcass, and bake them at 350 degrees F for a few minutes until the meat shows no sign of pink. Or microwave on High at 30-second intervals until the meat looks well done.