Melt butter in a small saucepan. Add flour and cook, stirring, 2 minutes. Drizzle in milk while stirring. When thickened, add egg yolks and cook, stirring, 1 minute. Add cheese a little at a time and stir until melted.
Beat egg whites in a large bowl until stiff peaks form. Fold cheese mixture into the egg whites, a little at a time. Scrape into the top of an ungreased double boiler. Set over barely simmering water. Cook, covered, about 1 hour. (Do not let water touch the bottom of the double boiler insert.). Serves 4 as a side, 2 as a main course.