HEAT grill to medium-high heat.
SHAPE meat into 4 (1/2-inch-thick) patties. Place mushrooms and onions on sheet of foil; drizzle with oil.
GRILL patties 5 to 6 min. on each side or until done (160°F). Meanwhile, grill vegetables (on foil) 4 to 5 min. or until crisp-tender; remove from grill.
TOP burgers with cheese. Place rolls, cut-sides down, on grill. Cook 1 min. or until cheese is melted and buns are lightly toasted.
MIX mayo, horseradish and chives; spread onto rolls. Fill with burgers and vegetables.
This recipe courtesy of kraftfoods.com