Preheat the oven to 180C/350F/Gas 4.
Place the butter and flour into the bowl of a food processor with the salt, cayenne, mustard powder and cheeses. Process together to begin with, and then finely pulse the mixture in short spurts as you notice the mixture coming together - it will eventually bind without the need for egg or water. Wrap in cling film and leave to chill in the fridge for at least 30 minutes.
Lightly flour a work surface and gently roll out the pastry to about the thickness of two pound coins. Cut out the biscuits to the size and shape you wish - anything between 3cm/1¼in and 5cm/2in, depending on the occasion. Lay them out on a greased baking tray about 2cm/¾in apart - it may take two lots of baking to use up the entire mixture.
Carefully brush the surface of each biscuit with the egg and sprinkle over a little finely grated parmesan. Bake for 10 minutes, or until they are a gorgeous golden-brown colour; the superb smell will also inform you that they are ready.
Carefully lift the biscuits off the tray using a palette knife and place on a rack to cool. Although the biscuits will keep well in a sealed container for a few days, I have never known this to happen!