1. Combine first 7 ingredients in a large stockpot over medium-high heat. Cook until salt is dissolved. Remove pan from heat; cool completely.
2. Remove and discard giblets and neck from turkey, or reserve for another use. Trim excess fat. Tie ends of legs together with kitchen twine. Lift wing tips up and over back; tuck under turkey. Add turkey to pan, turning to coat. Cover and refrigerate for 24 hours, turning the turkey occasionally.
3. Preheat oven to 450°.
4. Remove turkey from brine; discard brine. Rinse turkey with cold water; pat dry. Place turkey, breast side up, in a roasting pan. Pour 1 cup broth into pan. Bake at 450° for 30 minutes.
5. Reduce oven temperature to 350° (do not remove turkey from oven). Bake turkey at 350° for 1 1/2 hours or until thermometer inserted into meaty part of thigh registers 165°. Remove turkey from oven; let stand 30 minutes. Remove and discard skin.
6. Place a zip-top plastic bag inside a 2-cup glass measure. Pour drippings into bag; let stand 10 minutes (fat will rise to the top). Seal bag; carefully snip off 1 bottom corner of bag. Drain drippings into a measuring cup, stopping before the fat layer reaches the opening (reserve 1 tablespoon fat). Combine drippings, remaining broth, and cider in a small bowl. Place broiler pan on stovetop over medium heat, scraping to loosen browned bits. Weigh or lightly spoon flour into a dry measuring cup; level with a knife. Add flour and reserved fat to pan; cook 1 minute, stirring frequently. Slowly add broth mixture, stirring with a whisk; cook 4 minutes or until thickened, stirring occasionally. Stir in 1/4 teaspoon black pepper.