Mix the stout, wine, garlic and thyme in a bowl until well combined. Add the steak and venison. Cover and chill in the fridge overnight.
Remove the meat from the marinade and dredge it in half of the flour.
Heat half of the butter in a large heavy-based saucepan and brown the meat on all sides for 3-4 minutes. Remove and set aside.
Add the rest of the butter and fry the onion for 3-4 minutes. Add the remaining flour and cook for two minutes. Stir in the tomato purée and cook for a further six minutes.
Pour in the marinade a little at a time followed by the stock. Boil the mixture for 10-15 minutes, or until it becomes a thick sauce.
Add the meat to the pan with the bay leaf and cook for at least two hours, or until the meat is very tender. Set aside to cool, then stir in the oysters.
Preheat the oven to 180C/350F/Gas 4.
Roll out two-thirds of the pastry on a floured work surface and use it to line a large pie dish. Spoon the meat mixture into the pie dish.
Roll out the remaining pastry and use it to cover the meat mixture. Trim the pastry and crimp the edges. Brush the top of the pie with the beaten egg. Cut a small hole in the top of the pie to allow steam to escape.
Bake in the oven for 30-35 minutes, or until the pastry is crisp and golden-brown and filling is piping hot.