Preheat the oven to 400°F. Thoroughly butter a 7-inch diameter souffle dish, about 3 inches deep.

Melt the butter in a saucepan and mix in the flour. Cook together for a couple of minutes to make a roux, then gradually whisk in the milk until a smooth, very thick sauce is achieved. Remove from the heat and leave to cool slightly for a couple of minutes, then add the egg yolks one by one, beating them in thoroughly. Stir in the grated cheeses and season with salt and the cayenne. Pour into a roomy bowl, removing every last vestige of the mixture with a rubber spatula.

Whisk the egg whites in another bowl until firm. Stir a small amount into the cheese mixture to slacken it, then deftly fold in the rest of the whites, using a serving spoon or spatula.

Gently pile the mixture into the buttered souffle dish and sprinkle the surface with extra Parmesan. Bake in the oven for 30 to 35 minutes, or until well risen, and golden and crusted on the surface.