1. Remove the giblets, neck and tail piece from the turkey and reserve them for gravy, if desired.
2. Rinse the turkey inside and out with cold water.
3. In a large pot or 5-gallon bucket, stir the salt and 1 gallon of cold water together.
4. Carefully set the turkey into the water and cover the bird by 2 to 3 inches with cold water.
5. Refrigerate or set the turkey in a very cold (32 to 40 degrees F) place for 8 to 12 hours.
6. Remove the turkey from the brine, rinse well and pat dry with paper towels.
7. Let it sit out at room temperature for an hour, or an hour and a half at most.
8. Position a rack in the bottom of your oven and preheat to 450 degrees F.
9. In a large bowl, toss together the onion, carrots, celery, thyme, parsley, bay leaf and half the butter.
10. Pack the body and neck cavities loosely with this mixture.
11. Truss the legs together with kitchen twine and secure the neck flap to the back with a couple of trussing pins or sturdy toothpicks.
12. Rub the turkey with half of the remaining butter and set the bird on its side on a rack in a roasting pan.
13. Roast it for 15 minutes, then turn it onto its other side and roast for 15 minutes more.
14. Reduce the heat to 325 degrees F.
15. Soak a large piece of cheesecloth (enough to cover the turkey breast) in the remaining butter, turn the turkey breast-side up and place the cheesecloth over the breast.
16. Add 1/2 cup of water to the pan.
17. Continue roasting, basting with pan juices every 15 to 20 minutes, until an instant-read thermometer inserted into the breast registers 160 degrees F.
18. Check a meaty section of the thigh, as well; it should also register 160 degrees F.
19. If the breast is cooking too quickly, tent it loosely with aluminum foil.
20. Total roasting time should be about 2 1/2 hours.
21. Let the turkey rest for 20 to 30 minutes before carving.