For the pastry, blend the flour, butter cubes and salt in a food processor until the mixture resembles breadcrumbs.
Add the cheese, water and egg yolk and continue to blend until the mixture comes together as a dough.
Turn out the dough onto a lightly floured work surface and knead lightly for 3-4 minutes, or until smooth and elastic. Wrap the dough in cling film and chill in the fridge for at least one hour.
Meanwhile, for the filling, heat the oil in a frying pan over a medium heat. Add the beef mince, in batches if necessary, and fry for 6-8 minutes, turning once, or until browned all over. Remove from the pan and set aside (keep warm). Repeat the process with the remaining batches of beef mince.
Add the onion, carrot and celery to the pan used to fry the mince. Fry for 3-4 minutes, stirring well, until softened.
Return the mince to the pan and stir in the tomato purée, Worcestershire sauce and bitter ale. Bring the mixture to a simmer and cook, stirring regularly, for 8-10 minutes, or until the majority of the liquid has evaporated.
Preheat the oven to 200C/400F/Gas 6. Grease a 20cm-25cm/8-10in pie plate with butter.
When the dough has chilled, divide it in half. Roll out one half onto a lightly floured work surface until slightly larger than the pie plate. Carefully line the pie plate with the pastry, pressing it into the edges of the plate.
Spoon the filling into the pie case.
Roll the remaining dough out onto a lightly floured work surface until it is slightly larger than the pie dish.
Brush the rim of the pie case with a little of the egg wash. Place the pastry disc on top of the pie and press the edges together. Brush the pie lid all over with the remaining beaten egg. Prick the pastry all over several times with a fork.
Bake the pie in the oven for 35-40 minutes, or until the pastry is crisp and pale golden-brown. Serve with mashed potatoes and brown sauce.