Preheat the oven to 220C/200C Fan/Gas 7.
Season the beef with salt and pepper. Place a large frying pan over a high heat, add the oil and fry the beef on all sides until browned. Transfer to a baking tray and roast in the oven for 15â€“18 minutes. Turn the oven off and remove the beef. Leave to cool, reserving any cooking juices, and then chill in the fridge for at least 1 hour (see tip).
Next make the topping. Melt the butter in the same pan and fry the mushrooms over a high heat for 5â€“10 minutes â€“ you may need to do this in batches. Tip the mushrooms into a sieve set over a bowl to collect the juices and reserve these for the sauce. Transfer the mushrooms to another bowl and allow to cool before mixing with the Parmesan, tarragon, mustard and egg yolk. Season with salt and pepper and chill in the fridge for 30 minutes.
Line a baking sheet with baking paper. Sit the single 375g packet of pastry on a floured work surface and roll out to a square about 40cm/16in in size, then transfer it to the baking sheet. Place the cooked beef to one side of the pastry and spoon the mushroom mixture on top. Fold over the ends of the pastry and then fold the longest edge over the beef, sealing along the side with a little of the egg wash. Chill in the fridge for 30 minutes. While it is chilling, preheat the oven again to 220C/200C Fan/Gas 7.
Brush the top of the chilled beef Wellington with egg wash. Roll out the remaining half block of pastry and cut into 8 thin strips: lay 4 strips diagonally, and evenly spaced, across the top of the beef Wellington, and 4 strips across these to create a lattice pattern. Brush the lattice with egg wash and then roast in the oven for 30â€“35 minutes or until the pastry is golden-brown and crisp.
Meanwhile, make the tarragon sauce. Melt the butter in the same frying pan and fry the mushrooms over a high heat for 5â€“10 minutes or until the juices evaporate. Sprinkle in the flour and add the crÃ¨me fraÃ®che with the reserved mushroom juices (from the topping), the mustard and tarragon. Season with salt, pepper and sugar and bring to the boil, stirring. Simmer for 3 minutes until reduced slightly and add any beef juices from the original baking tray. Keep hot.
Allow the beef Wellington to rest, covered with foil, for 15 minutes before carving. Slice into thick slices and serve with the hot tarragon sauce.