Roast Turkey with Giblet Gravy

1. Remove the turkey from the refrigerator and let it sit at room temperature for up to 2 hours to take off the chill.
2. Position a rack in the lower third of the oven and preheat to 325 degrees F. Pat turkey dry all over with paper towels. Trim off and discard excess fat. Fold the wings underneath the back of the turkey to prevent their overbrowning. Lightly salt and pepper the turkey inside and out. Truss the legs together with butcher's string.
3. Place the turkey on a rack in a large roasting pan. Spread 2 tablespoons of the butter over the turkey breast. Dampen an 18-inch square of doubled cheesecloth and drape it over the turkey breast, leaving the drumsticks uncovered. Place the pan in the oven and roast the turkey for 30 minutes.
4. Meanwhile, in a small saucepan, combine the chicken broth, the remaining 6 tablespoons butter, the Port, and the peanut oil. Warm over low heat until the butter has melted.
5. At the 30-minutes mark, using a bulb baster, baste the turkey through the cheesecloth with some of the broth mixture. Continue to roast, basting every 20 minutes, for 1 1/4 hours. Add the onion and the carrots to the roasting pan, stirring to coat them with the drippings. Continue to roast, basting the turkey every 30 minutes with the remaining broth mixture and then with the accumulated pan juices, until the vegetables are well browned and an instant-read thermometer inserted into the thickest part of the turkey thigh away from the bone registers 165 degrees F, about 1 hour longer (for a total roasting time of about 2 1/2-3 hours).
6. Transfer the turkey to a cutting board and cover it loosely with aluminum foil while you make the gravy.
7. To make the gravy, place the roasting pan with the pan juices and vegetables over 2 burners and turn the heat to medium-high. Add all but 1/4 cup of the turkey stock to the roasting pan and bring to a brisk simmer. Stir to deglaze the pan, scraping up the browned bits from the bottom, about 5 minutes.
8. Pour the contents of the pan through a sieve set over a large bowl, pressing hard on the vegetables with the back of a large spoon to extract all the liquid; discard the solids. Spoon off as much of the fat from the liquid as possible, or pour the liquid into a fat separator and pour off the liquid. Transfer the liquid to a medium saucepan. Place over medium-high heat and simmer briskly for 5 minutes.
9. Finely chop the heart and gizzard reserved from making the turkey stock and the reserved uncooked liver. Reduce the heat to low and stir the giblets into the gravy. In a small bowl, stir the remaining 1/4 cup stock into the cornstarch to make a slurry. Gradually stir the slurry into the gravy. Cook until the gravy thickens, 3-4 minutes. Season with salt and pepper.
10. Carve the turkey and serve with the gravy.

Make-ahead tip: The stock may be made up to 3 days in advance and refrigerated, or up to 3 months before and frozen. Or, it may be made while the turkey sits before roasting.