Adjust an oven rack to the lowest position and heat to 425 degrees. Remove the neck and giblets and pat the turkey dry with paper towels. Trim the tailpiece, tie the legs together, and tuck the wings under the bird. Chop the neck and giblets into 1-inch pieces.

Spread the onions, carrots, celery, neck pieces and giblets (if using) in a large roasting pan. Line a V-rack with foil and poke several holes in the foil. Set the rack inside the roasting pan and coat the foil with vegetable cooking spray.

Brush the breast side of the turkey with half the butter, then season with salt and pepper. Lay the turkey in the rack breast-side down. Brush the back of the turkey with the remaining butter, then season with salt and pepper. Roast the turkey for 1 hour.

Remove the turkey from the oven. Lower the temperature to 325 degrees. Tip the juices from the cavity of the turkey into the pan. Flip the turkey breast-side up using clean potholders or kitchen towels. Continue to roast the turkey until the thigh registers 175 degrees on an instant-read thermometer (ignore any pop-up timer), about 1 to 2 1/2 hours longer. Add the broth as needed to prevent the drippings from burning.

Tip the turkey so that the juice from the cavity runs in to the roasting pan. Transfer the turkey to a carving board and let rest, uncovered, for 30 minutes before carving.

Meanwhile, use the roasted vegetables and drippings in the pan to make gravy