Wrap a piece of cooking yarn around both filets. This helps the meat stay nice and juicy after it's fried in the pan and it fits better inside the puff pastry.
Fry up both sides of the filets on high in the vegetable oil. Using a pair of tongs, you can grab the filets and fry the sides as well.
Now put the two beef filets to the side and add butter to the pan. First, sauté the onion in the fat, then add the chopped mushrooms. Now salt and pepper. Add the chopped garlic, followed by the sherry and thyme.
Place a sheet of puff pastry on a big piece of plastic wrap. Pile a little bit of the mushrooms on top. Put the beef tenderloin on top of the mushrooms and cut off the cooking yarn. The whole thing gets a dollop of mustard and another serving of mushrooms. Using the plastic wrap, wrap up the beef tenderloin.
Roll the puff pastry into a small ball. Don't worry: thanks to the plastic wrap nothing will fall out and you can seal the pastry shut without issue. Roll the puff pastry balls out of the plastic wrap and place them on a baking sheet. Coat them with whisked egg. Now you just have to bake them in the oven for 20 minutes at 430°F.