HEAT barbecue to medium-high heat.
MIX meat, egg and 2 Tbsp. barbecue sauce; shape into 4 patties.
GRILL patties, peppers and onions 5 min. on each side or until burgers are done (160ºF) and vegetables are softened and lightly charred, brushing burgers and vegetables occasionally with remaining barbecue sauce. Top burgers with Singles; grill 1 to 2 min. or until melted. Meanwhile, place buns, cut-sides down, on barbecue; grill until toasted.
SPREAD buns with dressing; fill with lettuce, burgers and vegetables.