1If using charcoal grill, place drip pan with 1/2 inch water directly under grilling area, and arrange coals around edge of firebox. Heat coals or gas grill for indirect heat.
2In small bowl, mix basil, rosemary, salt and pepper. Rub basil mixture over all sides of turkey. Insert barbecue meat thermometer so tip is in thickest part of turkey and does not touch bone.
3Place turkey, skin side down, on grill over drip pan or over unheated side of gas grill. Brush with dressing. Cover and grill over medium heat 30 minutes. Turn turkey; brush with dressing. Cover and grill 2 to 3 hours longer, brushing occasionally with dressing, until thermometer reads 170ºF and juice of turkey is no longer pink when center is cut.
4Remove turkey from grill; cover with foil. Let stand 10 minutes before slicing.