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Remove the bag of giblets and the neck from turkey; and, if you like, reserve for another use (you can freeze them, freezing the liver separately). Discard any large pieces of fat from the turkey, rinse the bird inside and out and place in the brine. Top with a weighted plate to keep it submerged. Refrigerate, or, if it is winter and you have an unheated garage, place it in there. A cooler, lined with a plastic bag works well too. Brine for 24 hours and up to 48 hours.
For roasting the bird: Preheat the oven to 450 degrees F. Lift the turkey from the brine; discard the brine. Rinse and pat dry. Pour 2 cups of water into the bottom of a large roasting pan. Place the turkey, breast-side up, on a rack in the pan. Place the lemon and orange in the turkey cavity. Tie the legs together with twine. Tuck the wings under. Rub the entire turkey with the oil.
Roast for 30 minutes, and then reduce the heat to 350 degrees F and continue roasting until an instant-read thermometer registers 160 degrees F in the thigh without touching the bone, 2 hours 15 minutes to 2 hours 45 minutes total (about 12 minutes per pound).
For the glaze: While the turkey is roasting, combine the cider, soy sauce and rosemary in a small saucepan and bring to a boil over high heat. Reduce the heat to medium and boil until the mixture is reduced to 3/4 cup, about 30 minutes. Baste the turkey with the glaze every 15 minutes during the final 45 minutes of cooking time.
Transfer the turkey to a platter or carving board and tent with foil. Rest the turkey for at least 30 minutes and up to 1 hour before carving.