Preheat the oven to 180°C/gas mark 4. Line 2 baking sheets with lengths of baking parchment.
Tip the flour and butter into a large mixing bowl. Rub the butter into the flour using your fingertips until the mixture resembles breadcrumbs. Add the cheddar and beaten egg and mix together with a wooden spoon until combined.
Sprinkle a little flour on to a work surface, then roll out the dough. Cut star shapes from the dough using a cutter. Lift them with a spatula on to the baking sheet, leaving a little space between them so they can spread out. Bake for 10-12 minutes until just golden. Remove from the oven and leave to cool on the trays for a couple of minutes, then transfer to a cooling rack.