Combine all brine ingredients, except ice water, in a stockpot, and bring to a boil. Stir to dissolve solids, then remove from heat, cool to room temperature, and refrigerate until thoroughly chilled.
Early on the day of cooking, (or late the night before) combine the brine and ice water in a clean 5-gallon bucket. Place thawed turkey breast side down in brine, cover, and refrigerate or set in cool area (like a basement) for 6 hours. Turn turkey over once, half way through brining.
A few minutes before roasting, heat oven to 500 degrees.
Remove bird from brine and rinse inside and out with cold water. Discard brine. Pat dry with paper towels. Add rosemary, bay leaves, thyme, lemons and orange to the cavity. Tuck back wings and coat whole bird liberally with olive oil.
Arrange the halved carrots, quartered onions and celery stalks on a half-sheet pan or baking sheet. Position the turkey on top of the carrots and celery so that the turkey does not rest directly on the bottom of the pan.
Roast on lowest level of the oven at 500 degrees F. for 30 minutes. Remove from oven and cover breast with double layer of aluminum foil, insert probe thermometer into thickest part of the breast and return to oven, reducing temperature to 350 degrees F. Set thermometer alarm (if available) to 161 degrees. A 14 to 16 pound bird should require a total of 2 to 2 1/2 hours of roasting. Let turkey rest, loosely covered for 15 minutes before carving.