Combine the onion, carrot, celery, bay leaf, and 2 sprigs thyme in the bottom of a roasting pan. Remove and discard the giblets from the turkey; reserve the neck and place in the bottom of the roasting pan to flavor the jus. Rinse the turkey with cold water then pat dry with paper towels. Trim any excess fat. Starting at the neck cavity, loosen the skin from the breast and drumsticks by gently inserting your fingers between the skin and meat and gently pushing. Lift the wing tips up and over the back then tuck underneath the turkey.
Combine the chopped sage, thyme leaves, butter, garlic, salt, and pepper in a medium bowl. Rub the mixture both under and over the skin. Place the remaining thyme sprigs and sage sprigs in turkey cavity; tie the legs together with kitchen string.
Place turkey breast side up on vegetable mixture in the roasting pan; pour in the broth. Roast 30 minutes; tent loosely with foil and roast 30 minutes longer. Reduce the oven temperature to 325°F and continue to roast, basting every 30 minutes, for 1 hour 20 minutes to 1 hour 25 minutes longer, until an instant read thermometer inserted into the thickest portion of the thigh registers 180°F. Transfer the turkey to a cutting board, cover with foil and let stand 30 minutes before slicing.
ForTurkey Gravyrecipe (recipe provided separately) Pour the pan drippings through a wire sieve into a fat separator, pressing on the solids with a rubber spatula; discard solids. Let the drippings stand 10 minutes; pour into a 4-cup measure and discard fat. Reserve the drippings forTurkey Gravy.