Make turkey: Preheat oven to 350°F. Combine butter, chopped thyme, and chopped sage in a bowl. Season with salt and pepper. Place thyme sprig, sage sprig, carrots, celery, onion, turkey neck, and 2 cups water in a roasting pan; top with a roasting rack.

Loosen skin on turkey breasts and rub butter mixture under skin. Season turkey, including cavity, generously with salt and pepper; place on roasting rack. Tie legs together with kitchen twine and tuck wings under.

Roast, basting every 30 minutes and adding more water to pan if vegetables begin to scorch, until an instant-read thermometer reaches 165°F when inserted into thickest part of thigh, about 2 to 3 hours. Transfer turkey to a cutting board; let rest 30 minutes before carving. Scrape brown bits from pan and reserve drippings and neck for gravy.

Make gravy: Cook reserved turkey drippings and turkey neck in a skillet over medium-high heat, stirring often, until dark brown and thickened, 12 to 14 minutes. Add white wine and simmer, stirring often, until syrupy, 6 to 8 minutes. Sprinkle with flour and cook, stirring briefly. Gradually stir in chicken stock and simmer until thickened, 14 to 16 minutes. Pour through a strainer. Season with salt and pepper.