Preheat oven to 325 degrees F. Rinse turkey with cold water, drain well, and pat dry with paper towels. Season inside the cavity with 1 teaspoon salt and 1/2 teaspoon pepper. Stuff cavity with onion and carrot, and tie legs together using butcher's twine. In a roasting pan fitted with a rack, place turkey breast side up. Rub butter under and over skin. Rub skin with 1 teaspoon each salt and pepper. Loosely tent turkey with heavy-duty aluminum foil. Roast turkey for 1 hour, then baste with pan juices. Roast for 1 more hour; then remove and discard foil and baste. Continue roasting, basting turkey every 30 minutes until an instant-read thermometer reaches 170 degrees F when inserted into thickest part of thigh, 3 1/2 to 4 hours total.