In a small skillet coated with cooking spray, saute mushrooms and onion for 3 minutes. Add garlic and oregano; saute 1-2 minutes longer or until onion is tender. Stir in tomatoes. Cook, uncovered, over medium-low heat for 5 minutes, stirring occasionally. Set aside and keep warm.
In a large bowl, combine mushrooms, basil, egg white, parmesan, breadcrumbs, salt and pepper. Crumble beef over mixture; mix well. Shape into 6 patties.
Coat grill rack with cooking spray before starting the grill. Grill patties, covered, over medium-hot heat for 4-5 minutes on each side or until meat juices run clear. Top patties with cheese and the tomato sauce. Serve over buns.