Using a food processor, mix flour, mustard, salt, black and cayenne peppers.
Add butter and pulse to form fine crumbs. Add cheese, pulse until finely chopped.
Add the egg and 4 tbsp cream, pulse just until a soft, crumbly dough forms. Add remaining cream if dough is dry.
Shape the dough into a disk, cover with plastic wrap and refrigerate for 30 minutes, until chilled.
Preheat oven. Lightly flour a work surface and roll out the dough to 1/4 inch thickness.
Using a floured biscuit cutter (or drinking glass) cut out round biscuits. Re-roll and cut scraps. (If desired, brush biscuits with a second, beaten egg).
Bake for 15-18 minutes, rotating pans once, until biscuits are crisp and golden. remove from pans and serve warm.