Preheat the oven to 180 C / Gas 4. Grease a large baking tray.
In a large bowl rub the butter into the flour until the mixture resembles fine breadcrumbs. Add the cheese and the egg, reserving a little egg for brushing. Knead until a dough forms. Turn out onto a floured surface and roll into a 2cm thickness. Cut into 6cm long strips and arrange on the prepared baking tray, spacing the straws 2cm apart. Brush with the remaining egg.
Bake for 20 to 25 minutes until golden brown. Remove from the oven and allow to cool slightly before serving.