Thaw the puff pastry according to the package (if using frozen).
Heat the olive oil in a cast iron pan (or other frying pan; do not use a non-stick skillet) over high heat. Season the filets with salt and pepper on both sides. Sear in the hot pan for 1-2 minutes on each side, making sure not to cook the steaks too much. Transfer to a plate and place in the refrigerator until ready to use. Do not clean the skillet.
In the same skillet, melt the butter. Saute the shallots until they are soft. Then add the minced garlic and mushrooms until they are soft, about 10-15 minutes. Season with salt and pepper and add the parsley. Remove from heat and allow to cool.
Roll out one sheet of puff pastry using a rolling pin. Place one of the seasoned steaks in the middle of the pastry. Using a sharp paring knife, you will cut out a large "+" shape (so the steak is in the middle of the cross/plus-sign). You will end up with 4 squares of extra pastry that you can save for another day or use for something else.
Add some of the mushroom mixture on top of the steak. Fold up the top, bottom and sides of the pastry and pinch to make sure there are no holes. Place seam-side down on a baking sheet and refrigerate or freeze until ready to bake.
Repeat with the other steak and sheet of puff pastry.
When ready to bake, preheat your oven to 350 degrees F.
Brush each pastry with the egg. Bake in your preheated oven for 30-40 minutes or until a thermometer inserted in the center of the steak reaches 130 degrees F for a medium rare steak. (If your wellington is frozen, heat your oven to 400 degrees F and bake for 20 minutes. Then turn the temperature down to 350 degrees F and bake for 35-40 minutes or until a thermometer reads 130 degrees F.)
Allow the beef wellington to rest for at least 10 minutes before cutting in half and serving.