Spray a 12-inch skillet with the cooking spray and heat over medium-high heat for 1 minute. Add the beef in 2 batches and cook until it's well browned, stirring often. Remove the beef from the skillet. Pour off any fat.
Reduce the heat to medium. Add the mushrooms and onion to the skillet and cook for 5 minutes or until the vegetables are tender. Stir in the vinegar and cook for 2 minutes.
Stir the sauce in the skillet and heat to a boil. Return the beef to the skillet. Top with the cheese. Cook and stir until the cheese is melted. Serve with the potatoes.