Remove giblets and neck from turkey; place in a large saucepan, adding bay leaf, 1 celery rib, and half the onion.
Add 6 cups water. Bring to a boil; reduce heat, and simmer, uncovered, 1 hour.
Pour through a strainer. (You should yield 3 cups; add water if necessary to measure 3 cups.) Set aside.
Rinse turkey with cold water.
Drain; pat dry.
Sprinkle body cavity with salt and pepper; place remaining celery rib and onion inside cavity. Close cavity; tie ends of legs together with heavy string. Tuck wingtips under bird.
Place turkey in a lightly greased roasting pan, breast side up. Rub turkey all over with 2 tablespoons softened butter; sprinkle with 1 teaspoon salt and 1/2 teaspoon pepper.
Roast, uncovered, at 325 until a meat thermometer reaches 180 in the thigh (about 3 hours), basting after 1 and 2 hours with remaining softened butter; turn turkey halfway through roasting. Baste frequently during last 45 minutes of cooking.
Add 1 cup reserved turkey broth to roasting pan during last half hour of roasting. If turkey starts to brown too much, cover loosely with aluminum foil.
Let turkey rest in pan 5 minutes; carefully remove to a serving platter or carving board. Cover with foil, and let rest up to 45 minutes.
Meanwhile, prepare gravy. Skim excess fat from pan drippings, if desired. Working over medium heat on the stovetop, whisk flour into pan drippings until smooth.
Whisking constantly, gradually add remaining 2 cups turkey broth; simmer 5 to 10 minutes or until gravy is thickened. Season with salt and pepper.
