Pat the turkey dry with paper towels. Place the wings underneath the body. Place the 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.
Finely chop the garlic, parsley, and sage. Combine in a small bowl with the lemon juice, zest, and 1 tablespoon of the olive oil. Carefully slide your fingers under the skin of the breast and thighs to loosen it. Stuff the herb mixture under the skin. 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.