Preheat the oven to 180°C, fan 160°C, gas 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 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 onto a work surface, then roll out the dough.
Cut star shapes from the dough, using a cutter, and lift them with a spatula onto the baking sheet, leaving a little space between them so they can spread out. Bake for 10-12 mins until just golden.
Remove from the oven and leave to cool on the trays for a couple of mins, then transfer to a cooling rack.