Break or cut off tough ends of asparagus. In 12x8-inch (2-quart) microwave-safe dish, arrange spears with tips in center. Add water; cover with microwave-safe plastic wrap. Microwave on HIGH for 3 to 4 minutes or until asparagus is crisp-tender.*
Meanwhile, in small bowl, combine mayonnaise, mustard and dill; mix well. Spread mayonnaise mixture evenly over cut side of each half of bread. Top each sandwich with mushrooms, cooked asparagus and bell pepper rings. Cut cheese into 1-inch-wide strips; arrange over peppers. Place on ungreased broiler pan or cookie sheet.
Broil 4 to 6 inches from heat for 1 to 2 minutes or until cheese is melted.