Slice potatoes and onions onto a 24x18-inch sheet of buttered heavy-duty foil.
Sprinkle with Parmesan cheese, salt, and pepper; mix lightly on foil.
Slice the 2 tablespoons butter over all.
Seal foil with double fold.
Place on grill; cook over slow coals till vegetables are tender, 50 to 55 minutes, turning often.