Preheat oven to 375°.
Combine the cider and 4 tablespoons corn syrup in a small saucepan; bring to a boil. Remove from heat; set aside.
Remove and reserve giblets and neck from turkey. Rinse turkey with cold water; pat dry. Trim excess fat. Lift the wing tips up and over back; tuck under turkey. Combine poultry seasoning, sage, salt, and pepper. Rub seasoning mixture into skin and body cavity. Place half of the garlic, onion quarters, and apple quarters into the body cavity. Place turkey, breast side up, in a shallow roasting pan coated with cooking spray. Arrange remaining garlic, onion, and apple around turkey in pan. Insert a meat thermometer into meaty part of thigh, making sure not to touch bone. Bake at 375° for 45 minutes. Baste turkey with cider syrup, and cover with foil. Bake at 375° an additional 2 hours and 15 minutes or until meat thermometer registers 180°, basting with cider syrup 4 times at regular intervals. Let stand for 10 minutes. Discard skin. Remove turkey from pan, reserving drippings for sauce. Place turkey on a platter; keep warm.
Strain drippings through a colander into a bowl; discard solids. 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 the drippings into a bowl, stopping before fat layer reaches opening; discard fat.
While turkey bakes, melt the butter in a medium saucepan over medium-high heat. Add the reserved giblets and neck; saute for 2 minutes on each side or until browned. Add broth, and bring to a boil. Cover, reduce heat, and simmer 45 minutes. Strain mixture through a colander into a bowl, discarding solids. Reserve 1/4 cup broth mixture. Combine the drippings and the remaining broth mixture in roasting pan on stovetop over medium heat, scraping the pan to loosen browned bits. Combine 1/4 cup reserved broth mixture and cornstarch; add to the roasting pan. Add 1 tablespoon corn syrup, stirring with a whisk. Bring to a boil; cook 1 minutes. Serve gravy with turkey (gravy will be dark and thin).