Melt butter in a heavy saucepan over low heat; add flour, stirring until smooth. Gradually add milk; cook over medium heat, stirring constantly, until thickened and bubbly.
Lightly beat egg yolks; gradually stir one-fourth of hot mixture into yolks; add to remaining hot mixture, stirring constantly. Cook, stirring constantly, until mixture thickens. Remove from heat, and stir in fish, salt, and pepper.
Beat egg whites (at room temperature) until stiff peaks form; fold into fish mixture. Spoon into six greased 6-ounce custard cups. Place custard cups in a 13- x 9- x 2-inch baking pan; pour hot water into pan to a depth of 1 inch.
Bake at 350° for 45 minutes or until browned. Remove cups from water; cool slightly. Invert each timbale onto an individual serving plate, and top with Mushroom Sauce. Serve immediately.