Remove the turkey from the refrigerator 45 minutes before roasting. Heat the oven to 425°F (220°C). Pat the turkey very dry with paper towels.
Mash the butter with the garlic, sage, rosemary, thyme, lemon zest, salt and pepper.
Gently loosen the skin over the breast with your fingers, without tearing it. Spread about two thirds of the butter under the skin, directly on the meat, and rub the rest over the outside.
Scatter the onion and carrots in a roasting pan and pour in the broth. Set the turkey on top, skin side up.
Roast for 20 minutes, then lower the oven to 350°F (175°C). Continue roasting for 60–80 minutes more, basting once or twice with the pan juices, until a thermometer in the thickest part (not touching bone) reads 160–165°F (71–74°C). Tent loosely with foil if the skin browns too quickly.
Transfer to a cutting board and rest for 20 minutes; the temperature will rise to at least 165°F (74°C). Carve and serve with the pan juices or gravy.