Preheat the oven to 200°C / fan oven 180°C / Gas Mark 6. Grease a 1.2 litre (2 pints) soufflé dish with butter, then add 2 tbsp of the grated Parmigiano Reggiano, tilting the dish so that it coats the base and sides.
Put the remaining butter into a saucepan with the flour and milk. Heat, stirring constantly with a small whisk, until the mixture is thick and smooth. Cook for a few more seconds, stirring all the time.
Remove from the heat and add the remaining grated Parmigiano Reggiano, stirring until melted. Season with a pinch of salt and cayenne pepper.
Stir the egg yolks into the cheese mixture. Whisk the egg whites in a large, clean bowl, using a hand-held electric mixer or whisk, until they hold their shape.
Fold them into the cheese mixture using a large metal spoon. Pour into the prepared dish.
Bake for 35-40 minutes, until risen and golden brown. Serve immediately.