Cook the butter and flour slowly together in the saucepan for 2 minutes without coloring. Off heat, beat in the boiling milk or cream, then the seasonings. Boil, stirring, for 1 minute. Sauce should be very thick. Taste for seasoning.
Remove sauce from heat. Place egg yolk in center of sauce and immediately beat it vigorously in with the wire whip. Beat for a moment to cool slightly, then beat in the cheese, and finally the butter. Taste carefully for seasoning. If not used immediately, dot top of sauce with butter to prevent a skin from forming.