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Heat oven to 220C/200C fan/gas 7. Unless the butcher has already done so, tie the meat around with string at even intervals to hold it together. Heat 2 tsp of the oil in a large non-stick frying pan. Lay the beef in the pan and fry over a high heat for 5 mins to seal, turning often. Transfer it to a roasting tin, season with pepper and a pinch of salt, then roast for 17-18 mins (this roasts to medium-rare).
Meanwhile, put the porcini in a small heatproof bowl, cover with boiling water and leave for 20-30 mins to soak. Pour 1 tbsp of the remaining oil into the same frying pan (don’t wash it) that the meat was cooked in. Tip in the shallots, garlic and chestnut mushrooms and fry for 4-5 mins, stirring often, over a high-ish heat, so all the liquid is first released from the mushrooms then evaporated, and all are softened. Remove from the heat, stir in the parsley and tarragon, season with pepper and a pinch of salt, and leave to cool.
Put the mix of leaves in a large heatproof bowl, pour over boiling water, leave for 30 secs, then tip into a colander, rinse under the cold tap and drain. Squeeze out all the moisture with your hands and pat dry with kitchen paper. Chop and set aside. Drain the porcini, reserving 5 tbsp of the soaking liquid. Chop the porcini finely and stir into the mushroom mix. Line a baking sheet with baking parchment.
When the beef is done, remove from the oven and let it sit in the tin for 10 mins for any juices to be released. Lower the oven to 200C/180C fan/gas 6. Lift the beef from the tin (keep all the juices in the tin for the gravy) and lay it on kitchen paper. Leave until dry and cool enough to wrap in the filo.
Lay 1 of the filo sheets on the work surface with the short end facing you. Brush all over with a little of the remaining oil (you will have 1 tbsp and 1 tsp left). Layer up and oil 4 more filo sheets in the same way. Remove the string from the cooled beef. Spread the chopped leaves down the middle of the pastry, so it is the same length and width as the fillet. Top with the mushroom mix and lightly press down. Lay the beef over this, with the top of the beef facing down. Bring the long sides of the filo over the beef to enclose it, then turn it over so the join is underneath. Tuck both ends of the pastry under (trim first if necessary to reduce any excess) and place on the lined baking sheet so all the joins are on the bottom. Brush with more oil.
Lay the last sheet of filo on the work surface in front of you, with one of the longest sides towards you, then cut across its width into 5 strips. Lay these one by one, slightly overlapping, over the wrapped beef, scrunching up an edge of each strip slightly as you go to give a bit of height. Carefully brush with the last of the oil, then bake for 30 mins until golden. If the pastry starts to brown too quickly, loosely lay a piece of foil over the top. Remove the meat and let sit for 5-10 mins before slicing.
Meanwhile, make the gravy. Heat the saved roasting juices in the roasting tin, stirring to deglaze. Stir in the flour. Gradually pour in the wine, stirring all the time to blend in the flour. Stir in the stock and reserved porcini liquid and bubble for about 8-10 mins to reduce a little. It should have body, but be thinner like a ‘jus’. Stir in the mustard and season with pepper. Transfer the beef to a platter, then slice thickly with a sharp knife and serve with a spoonful or two of the gravy.