Heat a cast iron skillet over medium-high heat. Add the vegetable oil and butter, heat until it just begins to smoke.
Generously rub the filet mignon on all sides with sea salt and pepper. Sprinkle with paprika.
Once the pan is very hot, sear the two filets 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 to a plate, and place 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, season with 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 all sides with the Dijon mustard.
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. Wrap in plastic wrap and place in the freezer.
Preheat the oven to 425 degrees. Line a baking sheet with parchment paper or foil.
Once the oven is hot, remove the beef from the freezer, unwrap and place on prepared baking sheet. Brush with the egg wash.
Bake for 25 minutes, or until a thermometer inserted into the middle of the steak reads 135 to 140 degrees (medium-rare) and the pastry is a deep golden brown.
Cut in half so you can see the intersection of steak, pastry and mushrooms. Serve with a side salad and glazed carrots.