Let turkey sit at room temperature at least 1 hour. Stuff turkey with aromatics or stuffing of your choice; tie the cavity closed.
Open grill vents. Place a chimney starter on the small lower grill grate, put 50 charcoal briquettes in starter, and ignite; let burn until ash gray. Remove chimney starter, center roasting pan on grate, and pour out coals, dividing evenly on each long side of pan. (Be careful not to spill ashes into pan, since it will collect the turkey drippings needed for gravy.) Top with main grill grate.
Combine oil, salt, and pepper in a small bowl. Rub or brush mixture all over turkey.
Place turkey on top grate, directly over roasting pan, and cover with grill lid (keep lid vent open). Every 45 minutes, add 8 unlit briquettes on each long side of roasting pan to keep heat even. (Some grills have a grate with space on the sides that allows for this addition. Otherwise you'll need a helper to lift the grate with the turkey while you add the coals.) Cook turkey until a thermometer inserted into the thickest part of the thigh (and the stuffing) reads 165 degrees, 2 to 3 hours (about 10 minutes per pound with aromatics, 12 minutes with stuffing). Remove from heat, and let rest 20 minutes before carving.
Recipe adapted from "Mad Hungry," by Lucinda Scala Quinn (Artisan Books). Copyright 2009. Now available in paperback.