Lightly butter a 2-quart soufflé dish. Cut a piece of aluminum foil long enough to circle the dish, allowing a 1-inch overlap. Fold foil lengthwise into thirds, and lightly butter one side. Wrap foil around dish, buttered side against dish, allowing it to extend 3 inches above rim. Secure foil with string. Set prepared dish aside.
Melt butter in a medium saucepan over low heat; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add milk; cook over medium heat, stirring constantly, until mixture is thickened and bubbly. Stir in salt and pepper; remove from heat, and set aside to cool slightly.
Beat egg yolks in a large mixing bowl until thick and lemon colored; add cooled sauce, mixing well with a wire whisk. Add chopped mushrooms and cheese, mixing well.
Beat egg whites (at room temperature) until stiff but not dry. Stir 1 cup beaten egg whites into sauce mixture. Gently fold remaining egg whites into sauce.
Spoon mixture into prepared soufflé dish. Bake at 375° for 45 minutes. Remove collar; serve immediately.