Preheat oven to 220ºC (200ºC fan assisted oven)/425ºF/Gas 7.
Heat the butter in a heavy based frying pan and quickly seal the steaks on all sides so they are just browning. Remove from pan and allow to cool on kitchen paper.
Add the onions to the pan and cook slowly for approximately 10 minutes until brown and tender, cool on kitchen paper.
Cut the pastry into 4 equal pieces and roll each one sufficiently large to be able to wrap up the steaks. Place one eighth of the onions in the centre of each pastry piece, top with a generous teaspoonful of horseradish and then sit a steak on top. Top the meat with the evenly divided remaining onions.
Brush the edges of one pastry piece with beaten egg and bring the sides up to meet over the meat. Press together firmly so that the filling is totally sealed in like a parcel, turn over and place on a lined baking sheet. Repeat with remaining pastry/steak stacks. Make 2-3 cuts in the tops of the parcels, brush with beaten egg.
Bake for 15 - 20 minutes until pastry is golden brown and depending on how rare you like the steak. Serve hot.