Make turkey broth: In a 6- to 8-qt. pot, bring turkey pieces, chicken broth, 1 1/4 cups wine, the carrots, onion, celery, thyme sprigs, and 1 tsp. each salt and pepper to a boil over high heat. Cover, reduce heat, and simmer until meat is tender when pierced, 1 1/2 hours. Strain broth into a bowl, pressing solids to extract juices, and discard solids. Measure 2 qts. broth and set aside. (Save extra for other uses.) Wipe pot clean with paper towels.
Set pot over medium heat, add flour, and cook, whisking constantly, until flour begins to smoke, smells slightly burnt, and has turned a rich medium brown, 10 to 15 minutes. (You'll use quite a bit of flour, since well-browned flour thickens less than raw flour.) Carefully whisk in 2 cups reserved broth and whisk into a smooth paste. Whisk in 1 1/2 qts. more broth, the remaining 1/4 cup wine, and chopped thyme. (Adding wine and herbs shortly before serving gives the gravy a big flavor boost.)
Bring to a boil over high heat, then simmer 5 to 10 minutes to blend flavors, whisking often. Season to taste with salt and pepper.
Make ahead: Up to 2 days, chilled. Reheat over medium heat, stirring.