Preheat the oven to 350°F. Put the butter and flour into a food processor, together with the salt, cayenne pepper, mustard powder, and cheeses. Briefly process all together to begin with, and then, finally, pulse the mixture in short spurts as you notice the mixture coming together-as pastry, if you like. Once the texture is clearly “clumpy,” tip it all out onto a lightly floured counter and deftly, but thoroughly, knead it together until well blended and smooth. Wrap in plastic wrap and chill in the refrigerator for at least 30 minutes.

Gently roll out the pastry on a lightly floured counter to about an 1/8-inch thickness. Using a 1½ to 2-inch cookie cutter, cut out crackers the size you wish for, depending on the occasion. Lay them out onto a greased baking tray about ¾ inch apart; it may be necessary to bake them in 2 batches.

Carefully brush the surface of each cracker with beaten egg and sprinkle a little finely grated Parmesan over. Bake in the oven for 10 minutes, or until a gorgeous, pale golden color is achieved; the superb smell will also inform you that they are ready. Carefully lift off the tray using a spatula and place on a cooling rack. Serve while still just warm, if possible.