Mix meat and mustard just until blended; shape into 16 (1-1/2-inch) patties. Place on rack of broiling pan sprayed with cooking spray.
Broil, 6 inches from heat, 6 to 8 min. or until done (160ºF), turning after 4 min. Top with Singles pieces; broil 1 min. or until melted.
Place cheeseburgers on 16 crackers; top with avocados, ketchup, aioli and remaining crackers to make 16 sandwiches.