The secret to this exceptional bird is an old-fashioned, inexpensive, enameled metal oval roaster with a lid, found in most supermarkets. It simultaneously roasts and braises the turkey, so the meat stays moist even as it cooks quickly. Uncover the pan at the end to crisp the skin.
This recipe has been adapted from the 2011 Gourmet Live Holiday Special Edition.
Preheat the oven to 400 degrees with the rack in the lower third.
Rinse the turkey inside and out, then dry well. Mix together the salt and pepper and rub all over the turkey inside and out. Put the onion and thyme in the large cavity. Pin the neck skin to the body with a metal skewer.
Center a 24-inch piece of kitchen string under the back of the breast and bring the ends over to pin the wings, then crisscross the string and tie the ends of the drumsticks together. Put the turkey on a flat metal rack in the roaster and brush with 4 tablespoons of the melted butter.
Cover the pan (or, if using an open roasting pan, cover the turkey with parchment paper, then foil) and roast for 1 hour. Baste the turkey with pan juices. Add water to the pan. Continue to roast, covered, until a thermometer inserted into the fleshy part of each thigh and thickest part of each breast and wings (test all; close to but not touching the bone) registers 165 degrees, 30 minutes to 1 hour.
Baste with the remaining tablespoon of melted butter and roast, uncovered, until the skin is browned, about 15 more minutes (total roasting time: 1 ¾-2 ¼ hours). Carefully tilt the turkey so that juices from inside the large cavity run into the pan. Transfer the turkey to a platter and let stand, loosely covered with foil, for 30 minutes (the temperature of the thigh meat will rise from 170-175 degrees).
Strain the pan juices through a fine-mesh sieve into a 2-quart measuring cup and skim off the fat (or use a fat separator), reserving the fat. Add the turkey stock.
Whisk together the flour and 1/3 cup reserved fat (if there is less, add melted butter) in a heavy medium-sized saucepan, then cook over medium heat, whisking constantly, for 2 minutes (mixture will be thick). Add the stock mixture in a fast stream, whisking constantly to prevent lumps, then bring to a boil, whisking. Stir in any turkey juices from the platter. Add the giblets (if using). Simmer the gravy, whisking occasionally, for 3 minutes. Season with salt and pepper, to taste.