PREHEAT greased grill to medium-high heat. Shape meat into four 1/2-inch-thick oval patties; set aside. Melt butter in small skillet on medium heat. Add mushrooms and onions; cook and stir 4 min. Stir in 1/2 cup of the barbecue sauce. Reduce heat to low; simmer 5 min. or until heated through, stirring occasionally.
MEANWHILE, grill patties 8 min., turning after 4 min. Brush with remaining 1/4 cup barbecue sauce. Top evenly with potatoes. Grill an additional 2 min.
SERVE topped with the mushroom mixture.