Bring 2 cups broth, reserved neck and giblets, and reserved trimmings to simmer in Dutch oven over high heat. Cook, adjusting heat to maintain vigorous simmer and stirring occasionally, until all liquid evaporates and trimmings begin to sizzle, about 20 minutes.
Continue to cook, stirring frequently, until dark fond forms on bottom of pot, 2 to 4 minutes longer.
Reduce heat to medium-high. Add onion, carrot, celery, parsley sprigs, thyme sprigs, garlic, pepper, and salt. Cook, stirring frequently, until onion is translucent, 8 to 10 minutes.
Stir in wine and bring to simmer, scraping up any browned bits. Add remaining 4 cups broth and bring to simmer over high heat. Reduce heat to medium-low, cover, and simmer for 1 hour.
Strain stock through fine-mesh strainer set over bowl; discard solids. (You should have 3½ to 4 cups stock. Turkey stock can be refrigerated for up to 2 days.)
Melt butter in medium saucepan over medium heat. Add flour and increase heat to medium-high. Cook, stirring constantly, until mixture is deep golden brown, 5 to 8 minutes.
Reduce heat to low and slowly whisk in strained stock. Increase heat to medium-high and bring to simmer. Simmer until thickened, about 5 minutes.
Add drippings, if using, and thin gravy with extra broth, if desired. Season with salt and pepper to taste, and serve.
Note: (Gravy can be refrigerated for up to 3 days or frozen for up to 2 weeks; to reheat, bring to simmer over medium-low heat, stirring occasionally.)
