Sauté mushrooms in 2 tablespoons butter in a medium skillet until tender; set aside.
Melt remaining butter in a 2- quart saucepan over low heat; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add milk; cook over medium heat, stirring constantly, until thickened and bubbly. Stir in wine, 1 cup cheese, and pepper. Set aside.
Chop half of ham slices; add chopped ham and sautéed mushrooms to cheese sauce. Line bottom and sides of a lightly greased 1-quart baking dish with remaining ham slices. Pour cheese mixture over ham, and sprinkle with remaining cheese. Bake at 350° for 20 to 25 minutes. Spoon hot over toast points.