In a small bowl, combine Monterey Jack cheese, Parmesan cheese, mayonnaise, onion and parsley; set aside.
Preheat broiler if necessary.
Place oven shelf 3 to 6 inches from heating element.
Cut crusts from bread; reserve crusts for another purpose.
Toast 1 side of trimmed bread slices.
Spread cheese mixture on untoasted side.
Broil until cheese mixture bubbles.
Cut each slice of bread horizontally into 3 thin strips.