Prep the pan: Preheat the oven to 425°F. Arrange the turkey pieces, onion, carrots, celery, and garlic in a large metal roasting pan or in a 9 x 13-inch pan. Drizzle with olive oil, season with salt and pepper, and toss to coat.
Roast: Roast, uncovered, for about 1 hour, turning the turkey and stirring the vegetables halfway through. The turkey should be well browned, and the vegetables should have caramelized edges.
Transfer: Move the turkey and vegetables to a Dutch oven or large pot.
Deglaze: While the pan is still warm, carefully pour in the white wine. Scrape the bottom of the pan with a wooden spoon to loosen the browned bits. Pour the wine, drippings, and browned bits into the Dutch oven.
Simmer the stock: Add 5 cups of the broth, the thyme, sage, and bay leaf. Bring to a boil, then reduce the heat to low. Simmer gently, uncovered, for 45 to 60 minutes.
Strain and skim: Pour the stock through a fine-mesh sieve into a large bowl or measuring cup, pressing gently on the solids. Discard the solids and skim the fat from the surface. Add enough of the remaining broth to measure 4 cups total.
Make the roux: Melt 3 tablespoons of the butter in a large saucepan over medium heat. Add the flour and cook, whisking constantly, for 2 minutes, until lightly golden but not browned.
Add the stock: Gradually whisk in the turkey stock. It will look lumpy at first, but keep whisking as you add it. Bring to a gentle boil, whisking frequently, then reduce the heat and simmer for 5 to 8 minutes, until smooth and thickened.
Finish: Remove from the heat and whisk in the remaining 1 tablespoon of butter. If any small lumps remain, strain the gravy once more through a fine-mesh sieve. Taste and season with more salt and pepper, if needed. Serve right away, or store it using the make-ahead steps below.