Slice bread in half lengthwise, leaving one side attached.
Open bread, butterfly fashion.
Combine mayonnaise, mustard, and onion powder in a small bowl, stirring well.
Spread over cut sides of bread; sprinkle with parsley and cheese.
Reassemble loaf, and wrap in heavy-duty aluminum foil coated with cooking spray.
Place on grill rack over medium coals; cook 10 minutes, turning after 5 minutes.
Cut bread into 4 slices.