Melt 1/2 of butter with olive oil in large sauté pan. Add mushrooms and green onions and sauté until tender. Add wine and white pepper, simmering until liquid is reduced. While mixture cooks, dredge chicken in eggs, then coat with bread crumbs.
Spray 9″ X 13″ baking pan with no-stick baking spray. Spoon the mushroom, onion mixture in bottom of pan in six piles. Place one chicken breast on top of each pile. Place remaining butter on top of chicken breasts. Cover and bake at 350 degrees for 40 minutes. Uncover and bake10 minutes longer or until chicken is browned.