Preheat the oven to 200°C/400°F/Gas mark 6. In a roasting tin, roast the beef in the middle of the oven for 25–30 minutes. Turn off the oven and allow the beef to cool completely, then discard the larding fat and strings. Skim the fat from the pan juices; reserve the juices.
In a heavy frying pan, cook the mushrooms in butter over a medium-low heat, stirring, until all liquid has evaporated and the mixture is dry. Season with salt and pepper and allow to cool completely.
Spread the beef evenly with the foie gras, covering the top and sides, and spread the mushrooms evenly over the foie gras.
On a floured work surface, roll the puff pastry into a rectangle of about 50cm/20in x 30.5cm/12in or large enough to enclose the beef completely. Invert the beef in the middle of the pastry, and fold up the long sides to enclose it, brushing the edges of the pastry with some egg white to seal. Fold the ends of the pastry over the beef; seal with the egg white.
Transfer the beef, seam side down, to a baking tin, and brush the pastry with the egg yolk wash. Chill for at least 1 hour.
Preheat the oven 200°C/400°F/Gas mark 6. Bake the fillet in the middle of the oven for 30 minutes. Reduce the heat to 180°C/350°F/Gas mark 4, and bake for a further 5–10 minutes until the pastry is cooked through. Leave to stand for 15 minutes.
In a saucepan, boil the reserved pan juices and the Madeira until the mixture is reduced by a quarter. Add the arrowroot mixture, stock and truffles. Season with salt and pepper. Cook the sauce over a medium heat, stirring, for 5 minutes or until thickened, being careful not to let it boil. Serve the beef cut into thick slices, accompanied by the sauce.