In a large saucepan, combine the butter, flour, salt and pepper over medium heat until smooth and butter is melted. Gradually add milk. Bring to a boil; cook and stir for 2 minutes or until thickened. Reduce heat. Add Swiss cheese; stir until melted.
Place bread in a shallow baking pan; top with the turkey, asparagus and about 1/2 cup sauce on each sandwich. Sprinkle with Parmesan cheese. Broil 4-6 in. from the heat for 4-6 minutes or until browned and bubbly.