Heat a stainless steel pan or cast iron skillet over medium-high heat. Add the vegetable oil and heat until just starting to smoke.
Rub the meat generously with salt and pepper.
Once the pan is very hot, sear the two filets very briefly on each side. You don’t want to cook the interior of the meat at this point, so it shouldn’t be more than a minute or two per side. Remove the filets from the pan and place on a plate in the freezer while you make the filling.
Let the pan cool slightly and turn the heat down to medium. Add the mushrooms, onion and garlic to the pan, and sprinkle on salt and pepper. Cook until the mushrooms release all their water and the onion is translucent.
Add the sherry and thyme. Cook until the sherry evaporates. Taste for salt and pepper, and season as necessary.
Remove from the heat and refrigerate until cold, then stir in the chopped parsley.
Roll out one puff pastry piece and cut in half, so you have two rectangular strips of dough.
Remove the steaks from the freezer and brush with the Dijon mustard on both sides.
Put a quarter of the mushroom mixture in the middle of one piece of the puff pastry. Top with one steak, then add a quarter more of the mushrooms.
Repeat with the other steak, puff pastry piece and mushrooms.
Fold the long sides of the pastry over the steak, tucking in and tightly sealing all the edges so the juice doesn’t escape. Wrapping it all in plastic wrap can help!
Preheat the oven to 425 degrees Fahrenheit and line a sheet pan. While the oven preheats, put the wrapped beef in the freezer.
Once the oven is hot, remove the beef from the freezer and put on the lined sheet pan. Coat with the egg wash.
Bake for 25 minutes, until a thermometer inserted into the middle of the steak reads 135 to 140 degrees Fahrenheit (medium-rare) and the pastry is a deep golden brown.
Cut in half so you can see the intersection of steak, pastry and mushrooms, and serve.
Make the puff pastry easier to work with by keeping it cold. That’s why this recipe calls for chilling the meat and filling in between steps!
The pan needs to be very hot in step 3 because it’s the key to searing the meat and subsequently adding flavor. If the pan isn’t hot, the meat either won’t brown, or it will take too long to brown and the middle will start to cook.
You can make this recipe ahead of time by following it up to step 9, then freezing until ready to bake. When you’re ready to cook, just put it in the oven directly from the freezer without thawing, and cook until the interior temperature of the meat is 135 to 140 degrees Fahrenheit (for medium rare), which may take longer than the 25 minutes.