To make the filling, melt half the butter with half the oil in a frying-pan.
Add the onion, garlic, and all the mushrooms and sauté for 10 minutes until tender and all the liquid has evaporated. Stir in the parsley, tip into a bowl, season and cool.
Season the steaks. Wipe out the same frying-pan and heat until hot. Add the remaining oil and sear the seasoned steaks for 20-30 seconds on all sides.
Cool, then spread over the pate. Cut the pastry into 4 pieces, roll out on a lightly floured surface to 8-10in squares and brush with beaten egg. Divide the mushroom mixture between the squares and place a steak on top, pate-side down. Bring up two opposite corners of the pastry square to overlap the steak in the centre, seal and gently tuck in the sides, brush with a little beaten egg, and bring the remaining two corners up and seal.
Place the parcels on a heated non-stick baking sheet, brush with beaten egg and bake in the oven for 25 minutes for medium-rare, or 5 minutes more for well done.
Place the frying-pan that you used to cook the steaks back on the heat. Pour in the wine and allow to bubble down, then simmer until reduced by two-thirds.
Just before serving, whisk in the remaining butter and season. Serve the beef wellingtons on warmed plates with the broccoli, and a little of the red-wine jus spooned over.