Preheat the oven to 220C/200C Fan/Gas 7. Heat the butter and oil in a non-stick frying pan. Add the mushrooms, then gently fry over a medium heat, stirring occasionally, until they have shrunk and the juices run out. Continue to cook until all the juices have evaporated. Tip into a bowl to cool.
Cut the steak into two even-sized pieces. Heat the pan, add the steak, and cook for a few seconds on each side to brown the outside - the meat should still be raw. Put on a plate and leave to cool.
Mix the pate with the cold mushrooms. Spread on top of the steaks. Cut the pastry in half and roll out to the thickness of a £1 coin. Place a piece of steak, pate-side down, in the centre of each half.
Dampen the edges of the pastry with a pastry brush, then fold over to enclose the steaks in neat parcels. Place the parcels on a baking sheet with the folds underneath. Brush with beaten egg, then bake for 18-20 minutes until golden. Serve with new potatoes sprinkled with chopped parsley, and carrot and courgette ribbons.