Heat a large frying pan with a little of the dripping or oil. Season the diced beef with salt and pepper. Fry in the pan until well coloured and completely sealed. Life out the meat and transfer to a large saucepan. Add a touch more oil, if necessary, to the frying pan. Season the kidneys and also fry quickly to seal and colour in the hot pan. Also transfer to the saucepan.
Melt a knob of butter in the pan and cook the onions and carrots in the melted butter for 2 - 3 minutes. They will lift any flavours left from the meats. Put into the saucepan with the meat. Fry the mushroom slices in a little more butter, just turning in the pan for a minute or two; keep to one side.
Place the saucepan on medium heat, stirring in the flour, and allow it to cook for 2 to 3 minutes. Add the tomato puree, bay leaf and mushrooms. Pour in the stock and bring to a simmer, skimming off any impurities. The meat should just be covered with the stock; if not, top with a little more stock or water. Simmer gently, partially covered, for 1 1/2 to 2 hours. During the cooking time it may need to be skimmed several times.
After 1 1/2 hours, check the meat for tenderness. If not quite soft enough, cook for the additional 30 minutes. If the meat is cooking gently, it will not need to be topped up with any additional stock or water. The sauce will have reduced, thickening it's consistency and increasing it's flavour.
Taste for seasoning, adding a dash or two of Worcestershire Sauce to the mixture. Transfer to a 2 pint pie dish and allow to cool to lukewarm.
Preheat the oven to 220°C/425°F.
Roll the pastry 1/4-inch thick. Cut a strip of pastry to sit around the rim of the dish. This will help the top to stay on. Brush the rim of the pie dish with some beaten egg and apply the strip. Brush again with egg. Making sure the pastry top is bigger than the dish, sit it on top. Push down around the sides, trim and crimp for a neat finish. Brush completely with egg wash and place in the preheated oven. Bake for 30 to 40 minutes until golden brown.