Preheat the oven to 200 ºC (400 ºF). Grease and dust a soufflé dish with grated parmesan cheese.
Melt the butter in a saucepan and add the flour. Mix until smooth and cook over low heat for 3 minutes. Have the milk ready at boiling point and add to the mixture. Whisk the mixture over low heat until smooth. Add the cheeses and season to taste.
Beat the egg yokes and mix into the cheese sauce Whisk the egg whites until stiff. Fold the egg whites into the mixture. Spoon the mixture into the prepared soufflé dish. Heat the grill of the oven and cook the soufflé under it for 4 minutes until a light crust forms. This will help the soufflé to rise evenly. Turn the grill off and bake the soufflé for 15 to 20 minutes at 200 º C (400 ºF) until well risen and golden brown. Do not open the oven during the cooking period. Remove from the oven and serve at once.