Heat oven to 425° F.
Rinse the turkey inside and out and pat it dry with paper towels. Place the wings underneath the body. If desired, tie the drumsticks together using 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 butter or oil and, using your fingers, spread it evenly. Season with the salt and pepper. Roast the turkey, uncovered, until browned, 30 to 45 minutes.
Add 1 cup cold water to pan. Cover the turkey loosely with foil. Reduce oven temperature to 350° F. Roast until a thermometer inserted in a thigh registers 180° F, about 2 hours total.
Let the turkey rest for at least 30 minutes before carving. Garnish with the orange wedges and parsley or celery leaves (if using). If making gravy, reserve the juices in the roasting pan.
Tip: To stuff or not to stuff? The safest place to bake stuffing is in a dish, says Diane Van, manager of the U.S. Department of Agriculture Meat and Poultry Hotline. If you prefer the added flavor that comes from cooking it in a turkey, leave it in the oven until the center of the stuffing registers 165° F.