Remove turkey from brine. Discard brine. Pat turkey dry inside and out with paper towels. Place, breast side up, on a rack set in a roasting pan. Let stand at room temperature for up to 1 hour.
Preheat oven to 375 degrees, with rack in lowest position. Fold a piece of cheesecloth (about 3 feet long) into thirds, place inside turkey cavity, and open up to create a pouch. Loosely fill cheesecloth pouch with stuffing (do not pack tightly), and tuck in ends of cheesecloth to close.
Tuck wings underneath the turkey, and tie legs together with kitchen twine. Brush turkey all over with butter, and season generously with salt and pepper.
Roast turkey, basting with pan juices every 30 minutes and rotating the pan after 2 hours, until a thermometer inserted into the thickest portion of the thigh registers 165 degrees, 2 1/2 to 3 hours. Remove stuffing pouch, and then empty it into a 9-by-5-inch loaf pan. Cover if desired, and return stuffing to oven; bake until it registers 165 degrees, about 30 minutes more. Transfer turkey to a platter, reserving pan juices for gravy. Let turkey stand for 30 minutes before carving.
Trussing the turkey ensures even cooking; lining the cavity with cheesecloth before adding the stuffing means easy removal later (simply transfer the stuffing to a baking pan, and return it to the oven to finish cooking while the turkey rests). To check for doneness, insert a meat thermometer in several different places; don't disregard the resting time, which allows the juices to redistribute.