1. To make the pastry – which can be made well ahead and stored in the fridge or frozen – stir the flour, thyme, salt, ground fennel and mustard powder in a large bowl or in the bowl of a standing mixer. Add the diced butter and margarine and process or rub with your fingers until the mixture resembles coarse breadcrumbs.
2. Beat the egg with the water and vinegar and gradually add to the flour mixture, stirring the liquid in with a large fork or a spatula. Add a little more water if it looks dry. When it starts clumping together, give it a short knead with your hands and gather the pastry into a ball. Divide it into halves; wrap both portions in cling film, flatten gently and chill for at least an hour.
3. Season the diced pork generously with pork as early as possible; it can sit in the fridge, salted, overnight if that’s feasible.
4. Heat up the oil in a large pan; add the pork and brown it well all over. Remove onto a plate.
5. Add the butter to the pan and follow with the girolles, when the butter foams. Fry them for a few minutes, stirring, over medium heat until a little coloured. Remove them with a slotted spoon onto the plate with the meat. Don’t worry if there are bits stuck to the bottom of the pan, the wet ingredients will help unstick them.
6. Add the onion to the pan, cover with a lid and cook over medium heat, stirring every now and then, until it softens. Add the apple and garlic and cook for a minute. Season with the white pepper, add the bay leaf and return the meat and mushrooms to the pan. Pour in enough water to only just come up to the level of the meat, bring to the boil then turn down the heat to a simmer. Cover with the lid and cook for 1 hour.
7. Check if the meat is tender; you might not need to cook it for an hour if using tender cuts of pork. If there’s still a lot of liquid in the pan, turn up the heat and cook it down for a couple of minutes. Stir the corn flour with a little cold water and add to the pan. Stir, let it bubble and take the pan off the heat. Leave it to cool completely – preparing the filling a day ahead is a good option.
8. When the filling is cold, prepare the pastry bottom and lid: roll out the bigger portion to a round of about 24cm in diameter, depending on the size and shape of your pie dish; it needs to cover the bottom with an overhang. Break the egg that will be used for brushing and use some of it white to brush over the bottom of the pie, to stop it from getting soggy. Return to the fridge while you roll out the lid to a slightly smaller circle; to cover the top.
9. Preheat the oven to 190C/200F/gas 5. Spoon the filling into the dish. Cover with the pastry lid, trim the excess pastry and fold the edges. Scrunch or crimp up the edge of the pie and brush the surface generously with the beaten egg. Cut slits to vent steam.
10. Bake the pie in the lower half of the oven for about 45 – 50 minutes until golden brown.
11. Let it stand for 5 minutes before serving, while you fry the remaining girolles, if using. Melt the butter in a small pan and stir fry the girolles for 5 minutes until coloured. Season them with salt and pepper and sprinkle with parsley. Spoon the girolles over pie slices and serve some green salad to go along with it.