About the ingredients
If you are making your own puff pastry, you'll need to do it a day ahead to give it plenty of time to rest. Otherwise, shop-bought pastry can be used, but be sure it's not a sweetened one intended for desserts. The mushrooms can be any combination of shiitake, girolles or wild mushrooms. At a pinch, you can use ordinary button mushrooms. The meat, well, it just has to be beef fillet - nothing else will achieve just-doneness in the time it takes for the pastry to cook.
Make the mushroom duxelle
Finely chop the onion and mushrooms, stir them together and add the pepper and thyme. You could use a blender or food processor to do the chopping, but you risk making a smoothie, which is not what we want! I/n a large frying pan, heat some vegetable oil to medium hot. Add the mushrooms and onions and cook, stirring occasionally, until almost all of the moisture has evaporated, about 10-15 minutes. You should be left with a thick paste. Put this in the fridge until you need it.
There shouldn't be any fat on your fillet steak, but there may be some silverskin. Trim this off with a small sharp knife. Heat some clarified butter in a heavy-bottomed frying pan or skillet, and sear the beef all over, including the ends. It should be lightly browned. Remove it from the pan and, while still hot, coat it with your favourite kind of mustard. Place in the fridge to cool.
Apply the duxelles
When the beef and the duxelles are cool, arrange several sheets of cling film on your worktop, overlapping them as necessary so that you get a sheet that is about twice as wide as your beef and several times longer. Spread the duxelle into a rectangle in the centre of the plastic. It should be the same width as the beef. Place the beef on this, pick up the bottom edge of the plastic, and roll it so that the duxelles covers the beef. Squidge up the ends of the film, and twizzle the whole thing in the air so that you have a tightly-wrapped package. Fold the two loose ends onto the top of the beef, and wrap tightly in more cling film. Place this in the fridge to chill for a couple of hours.
At this point, you should preheat your oven to 230°C (446°F).
Lightly flour your worktop and roll out the pastry into a sheet that is big enough to wrap the beef in. Trim the edges straight. Remove the plastic film from the beef/duxelles roll. Place the beef in the centre of the pastry sheet and roll the bottom edge of the pastry up so that it rests on the centre-line of the top of the beef. Roll the whole thing away from you, and cut the pastry so that you have a 2cm / 1 inch overlap. Unroll the package slightly, and moisten the top edge of the pastry with water. Now roll it back up, turn it over so that the seam is now on the top, with seal the edge with your finger. Cut away some pastry from each end of the roll so that you are left with two flaps. Moisten the edges of the flaps and fold them up towards the top of the package. Smooth out the seams with your finger as before.
Now, roll the whole thing over so that the seams are on the bottom. If you want to decorate your beef wellington, you can score lines and patterns into the pastry, and also make some holes in it to let the steam escape. Paint the whole thing with beaten egg, and bake for about 30 minutes.
When you take it out of the oven, let it rest for 10 minutes. Carefully cut into thick slices, serve with potatoes, vegetables and gravy, sit back and bask in the admiration of your guests.