Preheat the oven to 220°C (fan 200°C) and line a baking tray with parchment paper.
Sift the self-raising flour and baking powder into a large mixing bowl.
Add the cold butter and rub it in with your fingertips until the mixture resembles fine breadcrumbs.
Stir in the grated cheddar cheese, salt, mustard powder, and cayenne pepper.
Make a well in the centre and pour in the beaten eggs and most of the milk. Use a fork to mix quickly to a soft dough, adding the remaining milk if needed.
Turn the dough onto a lightly floured surface, knead it gently, and roll it out to about 2 cm thick.
Using the fluted cutter, press down firmly without twisting to cut out the scones. Place them on the baking tray.
Brush the tops of the scones with the reserved beaten egg using a pastry brush.
Bake in the preheated oven for about 10-15 minutes, until risen and golden brown.
Remove from the oven and cool on a wire rack. Serve warm with softened butter.