First, make the pancakes. Put the flour, egg and milk in a blender or food processor and whizz until smooth. Stir in half the butter, the tarragon and some seasoning. Heat a medium frying pan and brush with a little of the reserved melted butter. Pour in enough batter to make a thin layer in the pan and as soon as it sets, turn it over and cook the other side. Repeat with the rest of the batter until you have a batch of about 3-4 pancakes (any you don't use for the Wellington you can freeze).
Heat 2 tbsp olive oil and the tbsp butter in a large frying pan; add the mushrooms and fry until they have released all their liquid and become quite dry. Season. Clean the pan and heat the remaining oil. Sear the beef all over until it's nicely browned.
Lay a sheet of clingfilm on the work surface and lay out 2 or 3 pancakes, with each overlapping the other to make a rough rectangle that's a little longer than the piece of fillet
Spoon the mushroom mixture down the centre and lay the piece of fillet on top. Use the clingfilm to lift and fold the pancakes up and over the beef to make a parcel.
Roll the pastry out to a large rectangle, and lift the parcel of beef into the centre. Fold the bottom up and top down over it, trimming off any excess to a 2cm (½in) overlap.
Brush the edges with water and press firmly together. Fold the ends in, trimming off any excess. Place on a baking tray, seam-side down. Brush with egg and chill for 1 hour.
Preheat the oven to gas 6, 200C, fan 180C. Take the Wellington from the fridge and bake for 20 minutes, until the pastry is deep golden brown. To check if the beef is done, test it by sticking a metal skewer through the pastry and into the centre, then touch it against your wrist. If the skewer is cold, the beef will still be raw, so cook it for another 10 minutes.
Tip: Don't be tempted to skip the pancake stage, as they'll absorb the beef fillet's cooking juices, giving the pastry a lovely crisp finish. Cut pastry shapes to decorate if you like; just don't make them too thick
or they won't cook through.
See more Mother's Day recipes
For top tips on protecting you and your family when preparing raw meat and poultry, visit Food Safety in the Home and view the full Food safety at home video.