For the shortcrust pastry base, mix the flour, baking powder and salt together in a food processor. Add the butter and the egg yolk and pulse until the mixture resembles breadcrumbs. Gradually, with the motor running, add the water until the mixture comes together to form a dough (you may not need all of the water).
Roll the pastry dough into a ball and wrap in cling film. Chill in the fridge for one hour.
Meanwhile, for the pie filling, heat the vegetable oil in a large pan and brown the game and venison meat in small batches (be careful not to crowd the pan). Transfer the meat to a dish and set aside, repeating the process as necessary.
In the same pan used to cook the meat, add the bacon and the onions. Cook for 3-4 minutes, or until the onions are translucent. Add the celery and the mushrooms and cook for a further 3-4 minutes, or until tender.
Stir in the flour and cook for 1-2 minutes, mixing well to prevent any lumps from forming. Add the bay leaves, redcurrant jelly, stock, red wine and thyme. Season well with salt and freshly ground black pepper.
Bring the mixture to a simmer and cook, uncovered, for two hours, or until the meat is tender. Set aside to cool.
Meanwhile, preheat the oven to 180C/360F/Gas 4. Grease a 20cm/8in deep pie tin with unsalted butter.
Roll out the shortcrust pastry so that it is big enough to line the tin. Using a rolling pin, lift the pastry and place over the pie tin. Press the pastry down on the base and around the sides to line.
Line the pastry with baking parchment, then fill with baking beans. Bake in the oven for 20 minutes, or until the pastry is golden around the edges. Remove from the oven and set aside to cool. Remove the beans and discard the baking parchment.
Fill the pastry case with the cooled cooked game meat mixture.
For the pastry lid, roll out the sheet of puff pastry until it is large enough to fit over the pie dish. Paint around the edge of the pastry case with some of the beaten egg and place the sheet of puff pastry on top.
Crimp the pastry around the edges and trim off any excess. Prick the pastry several times with a fork to create holes for steam to escape. Decorate the top with the excess pieces of pastry (you can cut out leaves or other shapes).
Brush the pastry lid all over with the remaining beaten egg, then bake the pie in the oven for 30 minutes, or until the pastry is golden-brown and risen.
Set aside the pie to cool completely, then serve in thick slices, preferably with pickles.