Here's a couple more that work very well.
If the brine recipe requires bringing to a boil, I use half the amount of liquid (water/apple juice), then after it's off the boil, I add ice cubes/cold apple juice until I have the correct amount. This gets the temp down more quickly.
Keri C's Apple Juice Brined Turkey
1 gal apple juice,
3/4 cup Morton Kosher salt,
1/2 cup honey,
3/4 cup white sugar,
1/4 cup brown sugar.
Rinsed the bird VERY well inside and out with running water to remove all traces of the brine. Patted dry with towels and set to dry overnight in refrigerator. Went on smoker/BBQ at 6:45 am this morning stuffed with onions, over 2 chimneys burning Kingsford, cherry pellets, and dry foiled waterpan. No oil, rub, or anything else on the skin, which resulted in a very nice skin texture. Easily maintained between 325 - 340 with vents half open. Came off a few minutes after 10:00 am, probably a little overdone as part of the breast had already hit 165 but, hey, that's what brining's for, eh? Anyway, wrapped in about 8 layers of HD foil, 2 heavy towels, and set to rest breast side down in pre-heated ice chest. About 1 1/2 hours after it came off the smoker and it was still too hot to handle with plastic gloves.
Another apple-brined turkey recipe good for the smoker/BBQ
1 12-14 lb turkey
2 quarts apple juice
1 lb brown sugar
1 cup kosher salt
3 quarts water
3 oranges, quartered
4 ounces fresh ginger, sliced thin
15 whole cloves
6 bay leaves
6 large garlic cloves, peeled and crushed
vegetable oil or melted, unsalted butter
Combine apple juice, brown sugar, and salt in a large saucepan. Bring to a boil over high heat, stirring to dissolve. Boil for one minute, remove from heat, let mixture come to room temperature, then refrigerate to 40*F.
In a large non-reactive container, combine the apple juice mixture with the remaining ingredients and stir. Place rinsed, drained whole turkey into the brine. Use a heavy weight to keep the bird submerged, if necessary.
Refrigerate for 24 hours. Remove turkey from brine, rinse inside and out, and pat dry with paper towels. Fold wing tips under the bird. Brush outside surface with vegetable oil or melted butter.
Cook at 325-350*F to 160-165*F in the breast, 170-175*F in the thigh, approximately 2-1/2 to 3 hours. Cover loosely with foil and let rest 30 minutes before carving.