1. To prepare brine, combine first 9 ingredients in a large stockpot over high heat; cook 6 minutes or until salt dissolves, stirring occasionally. Remove from heat; add 1 gallon cold water. Cool to room temperature.
2. To prepare turkey, remove giblets and neck from turkey; reserve neck. Trim excess fat; add turkey to brine. Refrigerate 18 to 24 hours, turning occasionally.
3. Preheat oven to 375°.
4. Remove turkey from brine; discard brine. Pat turkey dry. Starting at neck cavity, loosen skin from breast and drumsticks by inserting fingers, gently pushing between skin and meat. Combine 3 tablespoons butter and next 3 ingredients (through 1/2 teaspoon pepper) in a small bowl; rub butter mixture under loosened skin and over breast and drumsticks. Lift wing tips up and over back; tuck under turkey. Place apple and next 5 ingredients (through onion) in the body cavity. Secure legs with kitchen twine. Place turkey on the rack of a roasting pan coated with cooking spray. Place neck in bottom of roasting pan; place rack with turkey in pan. Bake at 375° for 1 hour and 15 minutes. Cover turkey loosely with foil; bake an additional 45 minutes or until a thermometer inserted into thickest part of thigh registers 165°. Remove from oven; place turkey on a cutting board. Let stand, covered, for 20 minutes; discard neck and skin.
5. To prepare gravy, place a zip-top plastic bag inside a 2-cup glass measure. Pour pan drippings into bag; let stand 10 minutes (fat will rise to the top). Seal bag; carefully snip off one bottom corner of bag. Drain drippings into a small bowl, stopping before fat layer reaches opening; discard fat.
6. Melt 1 tablespoon butter in a medium saucepan over medium-high heat. Add thyme and shallot; sauté 2 minutes. Add 1/2 cup cider and bourbon; boil 3 minutes or until liquid is reduced by half. Combine 1/4 cup broth and flour, stirring with a whisk. Add flour mixture, remaining 1 cup broth, and drippings to pan; bring to a boil. Reduce heat, and simmer 4 minutes or until thickened. Stir in parsley and vinegar.