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Prepare up to a day ahead and chill. Remove from the fridge 1 hr before cooking, and allow an extra 5-10 minutes’ cooking time. The assembled wellington can also be frozen. Defrost in the fridge for 24 hrs and remove from the fridge 2-3 hrs before cooking.
Clean the mushrooms with a dry brush, discarding any dirt or woody stalks, and chop roughly if large. In batches, pulse in a food processor until finely chopped, without processing them to a paste.
Roll out the puff pastry to a 45cm x 35cm rectangle on a lightly floured surface then transfer to a large baking tray that’s been lined with baking paper, and chill in the fridge.
Make the savoury crepes first; place the flour in a large bowl and make a well in the centre. Add the egg and 100ml of the milk and gradually whisk into the flour; carry on adding the rest of the milk until you have a smooth batter. Season and whisk in 20g of the melted butter. Using a 20cm-base diameter nonstick frying pan, brush a little of the extra melted butter around the pan over a medium heat and carefully pour in just enough batter to make a fairly thin crepe. Cook for 1 minute on each side, and repeat until you have 4 evenly sized ones (the mix makes 5, to allow for any problems). Stack on a plate, separated by strips of baking paper; leave to cool.
You can skip the crepe making and use 4 ready-made classic pancakes
On a clean work surface covered with a sheet of baking paper, lay the 4 crepes into a rectangle shape of 35cm x 30cm, overlapping the bottom 2 onto the top 2.
In a large deep sauté pan, heat 2 tablespoons of oil; add the mushrooms and season. Cook on a high heat for about 20 minutes until there is no moisture at all left in the mushrooms; add the Madeira and reduce to a simmer.
Meanwhile, in a small pan, fry the shallots, garlic and thyme leaves with 1 tablespoon of oil until soft; add to the mushroom pan. When the Madeira has completely reduced and the mixture is almost dry again, check the seasoning. Remove the pan from the heat; quickly scatter the mushroom mix evenly over the pancakes. When the mushrooms have cooled, gently pat down.
Wipe out the pan and return to a high heat. Season the beef fillet well and rub all over with 1 tablespoon of oil. When the pan is smoking hot, lower the beef fillet in and sear all over for about 3 minutes, turning frequently, to just get a little colour all over. Transfer the beef fillet to a plate. When cooled, brush the beef all over with English mustard using a pastry brush. Lay horizontally across your mushroom mix.
Remove the pastry from the fridge, on its tray. Dust off any excess flour; brush all over with the beaten egg yolk mixture. Roll the beef up into a tight cigar shape inside the mushroom-topped crepes, tucking in the ends. Using the baking paper to lift it, transfer the wrapped beef to lie along one of the longest sides of pastry, about 5cm in from the edge.
Roll the pastry inwards, keeping it tight to the beef until the seam is across the bottom on the tray and with about 3cm of overlapped pastry; trim off any excess.
Carefully crimp down each end of the wellington and trim so there is just enough to tuck back under itself, then brush all over with more egg yolk. Any of the trimmed pastry can be used for decoration. Put the wellington in the fridge for 2 hours to rest and chill and then remove and give a final brush with egg yolk and sprinkle with mixed sesame seeds and a little sea salt.
Preheat the oven to 200°C, fan 180°C, gas 6 and bake the wellington for 50-60 minutes or until the centre reads 50°C (for rare) with a temperature probe, 60°C for medium-rare, 65°C for medium, 70°C for medium-well done, or 75°C for well done. The cooking time will vary according to the shape and thickness of your beef fillet.
Slide the cooked wellington onto a cooling rack over a tray, without its baking paper, and rest for at least 25 minutes before serving – don’t skip this step, as the meat is both finishing cooking, and resting to remain succulent. Transfer to a board then slice with a sharp serrated knife. If any resting juices leak, pour these into your gravy. Serve with gravy, roast potatoes and vegetables.