For the filling, pour 1 litre/1¾ pints cold water into a medium pan and bring to the boil. Peel the potatoes and cut into roughly 5mm-thick slices. Carefully drop the potatoes into the hot water and return to the boil. Cook for 4–5 minutes, or until just tender but not breaking apart. Drain in a colander and rinse under cold running water until cold. Leave to drain.
Melt 25g/1oz of the butter in a large non-stick frying pan and put the rest back in the fridge. Fry the onion over a medium heat for 5 minutes, or until fairly soft and lightly browned, stirring regularly. Remove from the heat.
Preheat the oven to 200C/180C Fan/Gas 6. Put a baking tray in the oven to preheat.
To make the pastry, put the flour, butter and cheese in a food processor and pulse until the mixture resembles fine breadcrumbs. With the motor running, add the beaten egg and water and process just until the mixture starts to come together. Add an extra 2–3 tablespoons cold water, if needed to bring the dough together.
Remove the blade and take the pastry out of the food processor. Knead lightly until the dough forms a ball. Weigh the pastry and take off 250g/9oz for the pie lid. Roll into a ball and set aside. Gather the rest of the pastry into a ball and flatten slightly.
Roll the flattened pastry out on a lightly floured surface, turning every couple of rolls until around 4mm thick and 4cm/1½in larger than a 23cm/9in round pie dish. Lift the pastry over the rolling pin and drop gently into the pie dish. Press the pastry firmly into the base of the dish and up the sides, making sure there are no air bubbles. Leave the excess pastry overhanging the sides.
Arrange a third of the cooled potato slices in the pie dish, dot with a third of the reserved butter and season with salt and pepper. Scatter half of the fried onions over the top. Add another third of the potatoes and butter; season well and top with the rest of the onions. Finish with the remaining potatoes and butter and more seasoning. Brush the rim of the pastry with beaten egg.
Roll out the reserved ball of pastry in the same way to make the pie lid. Cover the pie with the pastry lid and press the edges together firmly to seal. Trim the edges with a knife and crimp if you like. Make a couple of small holes in the centre of the pie with the tip of a knife. Brush the top of the pie generously with beaten egg.
Bake on the preheat tray in the centre of the oven for about 45 minutes, or until the pie is golden-brown all over and the potatoes are soft and piping hot. (You can check that the potatoes are ready by poking a skewer through the hole in the top of the pastry – it should slide in easily.)
Meanwhile make the bourguignon. Heat the olive oil in a large ovenproof casserole and add the shallots and carrots. Fry over a high heat, stirring regularly, until they are dappled with dark brown patches.
Sprinkle over the sugar and continue to cook for another couple of minutes to help caramelise. Remove from the casserole and set aside.
Add the sunflower oil and butter to the casserole. When it starts to foam, add the mushrooms and cook on a high heat until they have reduced down (you might need to do this in batches). Return the onions and carrots to the casserole and season generously with salt and pepper.
Add the herbs, then pour in the red wine. Bring to the boil and leave to bubble until the wine has reduced by at least a third. Add the stock, mushroom ketchup and mustard and stir until completely combined.
Return to the boil, then turn down to a simmer and cover with the lid. Cook for half an hour, until the vegetables are completely tender. Remove the thyme stalk and bay leaves.
Preheat the grill to high.
Mix the crumbled crumbled cheese with the crushed crisps. Sprinkle over the mushroom bourguignon and put under the grill for a few minutes until the cheese has melted.
Serve a slice of the pie with the cheesy mushroom bourguignon. Garnish with the chopped parsley.
