In a large saucepan, melt 2 tablespoons butter. Whisk in the flour, salt and pepper until smooth. Gradually stir in milk. Bring to a boil. Cook and stir for 2 minutes or until thickened and bubbly. Remove from the heat. Stir in cheese; set aside. , In a large skillet, saute ham and onions in 3 tablespoons butter until onions are tender. Add eggs; cook and stir until eggs are almost set. Stir in mushrooms and cheese sauce. Transfer to a greased 11x7-in. baking dish. Melt remaining butter; toss with bread crumbs. Sprinkle over top. Cover and refrigerate for 2-3 hours or overnight. , Remove from the refrigerator 30 minutes before baking. Bake, uncovered, at 350° for 25-30 minutes or until top is golden brown. Sprinkle with additional green onions if desired.