In a large nonstick skillet, cook the sliced mushrooms in 2 tablespoons of melted butter over medium-high heat, stirring constantly, for 3 to 5 minutes or until they become tender. Remove from heat and set aside.

Cut each chicken breast in half lengthwise. Place the chicken between two sheets of heavy-duty plastic wrap and flatten to a thickness of 1/8 inch using a meat mallet or rolling pin.

Dredge the chicken pieces in flour, ensuring they are evenly coated. In a large nonstick skillet, cook the chicken in batches, using 1 to 2 tablespoons of butter over medium heat for 3 to 4 minutes on each side or until they turn golden. Place the cooked chicken in a lightly greased 13 x 9-inch baking dish, overlapping the edges. Repeat the procedure with the remaining chicken and butter, reserving the pan drippings in the skillet. Sprinkle the sautéed mushrooms evenly over the chicken.

Add the Marsala wine and chicken broth to the skillet. Bring the mixture to a boil, then reduce the heat and let it simmer, uncovered, for 10 minutes, stirring occasionally. Stir in the salt and pepper. Pour the sauce over the chicken in the baking dish.

Combine the shredded mozzarella and Parmesan cheeses with the chopped green onions, then sprinkle this cheese mixture over the chicken.

Bake the dish uncovered at 450°F (230°C) for 12 to 14 minutes or until the cheese has melted and turned golden.

Serve the Chicken Lombardy hot and enjoy the tantalizing flavors of Italy.