In a medium bowl, stir the seasonings into the softened butter.
Place the turkey on a rimmed baking sheet. Remove the neck and giblets from the cavity (reserve for stock; see Make Turkey Stock below). Starting at the neck end, carefully slide your fingers under the skin, separating it from the breast and thigh meat. Use your fingers to spread the butter mixture under the skin. Sprinkle a big pinch of salt in the cavity, then rub the remaining salt over the entire bird on top of the skin. Refrigerate, breast side up and uncovered, 24 hours. (The skin will become taut, which means the dry brine is working.) Can be made 2 to 3 days ahead and kept refrigerated, covered, then uncovered for the last 24 hours.
Let the turkey stand at room temperature 1 hour. Position a rack in the lower third of the oven; preheat to 425°. Place the turkey, breast side up, on a rack in a roasting pan, then use paper towels to pat the turkey dry. Stuff the cavity with desired seasonings. Tie the legs together with a piece of kitchen twine. Rub the EVOO evenly over the skin.
Cover ends of drumsticks with foil. Roast the turkey 30 minutes. Reduce the oven temperature to 350° and continue roasting until an instant-read thermometer inserted in the thickest part of the thigh, not touching bone, registers 155° (the temperature will rise about 10° as it rests), 2 to 2 1/4 hours longer. Using a spatula and tongs (see Lifting the Turkey below), tilt the turkey to drain any juices from the cavity into the pan. Transfer the turkey to a cutting board; tent with foil and let rest 30 minutes.
Meanwhile, pour the drippings and solids from the roasting pan into a liquid measuring cup. Let the liquid settle; use a large spoon to skim off the fat and discard. You should have about 1 3/4 cups of skimmed drippings. Return the drippings to the roasting pan.
Carve the bird, adding the juices that accumulate on the cutting board to the roasting pan. Tent the turkey pieces with foil until ready to serve.
In a medium bowl, gradually whisk 1/2 cup chicken stock into the flour to make a paste. Set the roasting pan on two burners over medium. Bring to a simmer, scraping up any browned bits with a wooden spoon. Whisk in the flour paste and return to a simmer, whisking constantly. Gradually whisk in the remaining 1 cup stock and 1 1/2 cups water. Cook, whisking often, until thickened, 7 to 10 minutes. Season with pepper. Makes about 4 cups gravy.
Make Turkey StockDon't toss the neck and giblets that are tucked inside your turkey. Put everything but the liver (which is too pungent for stock) in a pot with 4 cups water, 1 carrot, 1 rib celery and 1 halved onion, and simmer while the turkey roasts. Strain the stock and use it in your gravy.
Lifting the TurkeySlide a pair of tongs into the cavity and open them to steady the bird. Use a sturdy spatula underneath.