Preheat the oven to 200°C (180°C Fan) and line a baking tray with baking parchment.
Rub the chilled butter into the flour until the mixture resembles fine breadcrumbs.
Mix in the cheddar, mustard powder, cayenne pepper, and salt.
Gradually add the cold water until a soft dough forms.
Roll the dough into a rectangle about 3mm thick.
Brush with beaten egg and sprinkle over the extra grated cheddar and black pepper.
Cut into long strips and gently twist each strip.
Arrange on the prepared baking tray, leaving space between each straw.
Bake for 12–15 minutes until puffed, crisp, and golden brown.
Transfer to a cooling rack and allow the cheese straws to cool slightly before serving.