Pre-heat the oven to 220C/425F/Gas 7. Line a baking tray with parchment paper.
Place both flours, baking powder, salt, cheddar and half the parmesan into a large bowl and mix to combine. Add the milk and bring the ingredients together with your hands or a wooden spoon. The mixture will be sticky at this point.
Tip the mixture onto a lightly floured surface. Fold and knead to form a soft dough.
Flatten or lightly roll the dough to 2.5cm/1in thick. Dredge a 6cm/2½in cutter in flour to ensure a precise cut and cut out 15 scones. Place them onto the baking tray – you may need to do this in two batches. Brush the tops of the scones with the beaten egg and sprinkle with the remaining parmesan.
Cook for 15-17 minutes until the scones are risen and golden-brown. Serve warm with butter.