Pat the turkey dry with paper towels. Place the wings underneath the body. Place the rosemary and parsley in the cavity. If you like a tidy-looking bird, tie the drumsticks together using the kitchen string.
Place the carrots, celery, and onions in a metal roasting pan. Transfer the turkey to a wire rack and place it on top of the vegetables. Drizzle the skin with the oil and, using your fingers, spread it on evenly. Season with 1 1/2 teaspoons salt and 1/2 teaspoon pepper. Roast the turkey uncovered until browned, 30 to 45 minutes.
Add the broth to the pan. Cover the turkey loosely with foil. Reduce oven temperature to 350° F. Roast until a thermometer inserted in a thigh registers 165° F, about 2 hours. Let the turkey rest for at least 30 minutes before carving. Reserve the pan drippings and vegetables for the gravy.