Lightly grease a baking tray. Sift the flour and a pinch of salt into a large bowl. Using your fingertips, rub in the butter until the mixture resembles fine breadcrumbs. Make a well in the centre and add almost all the water. Mix together with a flat-bladed knife, using a cutting action, until the mixture comes together in beads. Add a little more water if the dough is too dry. Turn out onto a lightly floured work surface and form into a ball. Cover with plastic wrap and refrigerate for 20 minutes.
Preheat the oven to 210°C (415°F/Gas 6–7). Mix together the steak, potato, onion, carrot, worcestershire sauce and stock in a bowl and season well.
Divide the dough into six portions. Roll out each portion to 3mm (⅛inch) thick. Using a 16cm (6¼inch) diameter plate as a guide, cut six circles. Divide the filling among the circles.
Brush the edges with beaten egg and bring the pastry together to form a semicircle. Pinch the edges into a frill and place on the tray. Brush the pastry with beaten egg and bake for 15 minutes. Reduce the oven to 180°C (350°F/Gas 4) and cook for 25–30 minutes, or until golden.