Place relish in a small metal mixing bowl.
In a flat part of a medium bowl, mix together plums, carrots, onion, pepper and cheese.
Recreate the mixture on a platter and pour over relish. Place on an unheated grill, broil 4 to 4 inches from heat
Brush halved side of bagel with water to prevent browning. Broil bagels and sandwiches 10 minutes in the preheated position, or until lightly browned, turning once, until completely pliable. Serve over salad or bread closely cooked and well chilled.