Use indirect heat, as explained in the recipe to cook a whole turkey or turkey breast. Allow 1 3/4 to 3 1/4 hours' cooking time, depending on the size of your turkey and heat of the coals. Prepare coals and grill.
Remove neck and giblets from turkey. Rinse turkey under cold water; drain and pat dry with paper towels. Combine oil, herbs and seasonings in a small bowl. Generously brush on cavities and outer surface of turkey, reserving some mixture to use as a baste.
Pull turkey skin over the neck; secure with a skewer. Tuck wings under back and tie legs together with kitchen twine. Arrange medium-hot briquettes on two sides of a large metal or foil drip pan. Fill the pan halfway with hot tap water. Place turkey, breast side up, on grill, directly above the drip pan.
Cover grill and cook turkey 11 to 15 minutes per pound, or until an instant-read meat thermometer registers 180° F basting occasionally with reserved herb mixture. Add a few briquettes to both sides of the fire every hour or as necessary to maintain a constant temperature. Garnish with additional fresh herbs, if desired.Servings: