1. To prepare brine, combine 2 cups water, 1/2 cup sugar, and next 4 ingredients (through bay leaves) in a saucepan over medium-high heat. Bring to a boil, stirring until salt dissolves. Remove from heat; let stand 10 minutes. Add sugar mixture and remaining 1 gallon water to a brining bag.
2. Remove giblets and neck from turkey; reserve neck. Trim excess fat; add turkey to brining bag. Seal bag; refrigerate 18 to 24 hours, turning occasionally.
3. Preheat oven to 500°.
4. Remove turkey from brine; discard brine. Pat turkey dry. Lift wing tips up and over back; tuck under turkey. Place parsley, 2 sage leaves, 3 celery pieces, 3 carrot pieces, 1 onion quarter, 2 apple quarters, and 2 lemon wedges in body cavity. Secure legs with twine. Place turkey on the rack of a roasting pan coated with cooking spray. Place turkey neck and remaining celery, carrot, onion, apple, and lemon in bottom of roasting pan; place rack with turkey in pan.
5. Bake at 500° for 45 minutes. Reduce oven temperature to 350° (do not remove turkey from oven). Place a foil tent over turkey breast. Pour 2 cups water in bottom of pan. Bake turkey at 350° for 45 minutes. Combine 1 1/2 cups stock and butter. Rotate turkey, and baste with 1/2 cup stock mixture. Bake 30 minutes; rotate turkey and baste with 1/2 cup stock mixture. Bake an additional 30 minutes or until a thermometer inserted into thickest part of thigh registers 160°. Remove from oven; place turkey on a cutting board. Baste with remaining 1/2 cup stock mixture. Let stand, covered, for at least 30 minutes; discard neck and skin.
6. Combine remaining 1/2 cup stock and flour, stirring with a whisk. Pour pan drippings through a sieve over a bowl; discard solids. Add flour mixture to drippings, stirring with a whisk. Place mixture in a medium saucepan; bring to a boil. Cook 2 minutes or until mixture thickens. Stir in ground pepper and 1/4 teaspoon salt. Serve gravy with turkey.