Preheat oven to 500°.
To prepare the turkey, remove giblets and neck from turkey; reserve for gravy. Trim excess fat. Stuff body cavity with 4 thyme sprigs, sage leaves, garlic, and medium onion. Tie legs together with kitchen string.
Starting at neck cavity, loosen skin from breast and drumsticks by inserting fingers, gently pushing between skin and meat. Combine butter, 1 1/2 teaspoons salt, and 3/4 teaspoon pepper. Rub butter mixture under loosened skin over breast and drumsticks. Lift wing tips up and over back; tuck under turkey. Pour 1 cup water in bottom of a roasting pan. Place roasting rack in pan. Arrange turkey, breast side up, on roasting rack. Bake at 500° for 30 minutes.
Reduce oven temperature to 350° (do not remove turkey from oven).
Bake turkey at 350° for 1 1/2 hours or until a thermometer inserted into meaty part of thigh registers 165°. (Shield turkey with foil if it browns too quickly.) Remove turkey from the oven; let stand 20 minutes. Discard skin before serving. Reserve pan drippings for gravy.
To prepare gravy, while turkey roasts, heat a large saucepan over medium-high heat. Coat pan with cooking spray. Add reserved turkey neck and giblets to pan; cook 5 minutes, browning on all sides. Add 4 cups water and next 7 ingredients (through bay leaf); bring to a boil. Reduce heat, and simmer until liquid is reduced to about 2 1/2 cups (about 1 hour). Strain through a colander over a bowl. Discard solids. Return mixture to the saucepan; stir in 1/2 teaspoon salt and 1/2 teaspoon pepper.
Place a zip-top plastic bag inside a 2-cup glass measure. Pour turkey pan drippings into bag; let stand 10 minutes (fat will rise to the top). Seal bag; carefully snip off 1 bottom corner of bag. Drain drippings into strained stock in saucepan, stopping before fat layer reaches opening; discard fat. Combine 1/2 cup stock mixture and flour in a small bowl, stirring with a whisk until smooth. Stir flour mixture into stock; bring to a boil, stirring frequently. Reduce heat, and simmer 3 minutes or until slightly thickened. Remove from heat; add oil, stirring with a whisk. Serve gravy with turkey.