If the tenderloin is uneven, tuck the smaller or narrow end under itself. You want the tenderloin to be even in thickness so it bakes evenly.
Tie the tenderloin into a log in about 6 places with kitchen twine so it keeps its shape while searing. Then, generously season the beef tenderloin with salt and pepper on all sides.
Heat oil over high heat in a large oven-safe skillet. Once the oil is hot, place the tenderloin in the pan. Turn the heat down to medium-high and cook for two minutes per side or until well-seared. Transfer to a plate, let it cool slightly, and remove the twine.
Optionally, brush the seared tenderloin with Dijon mustard all over.
Lay a long plastic wrap on the board or work surface. It should be about 15 inches wide and long.
Carefully place the prosciutto slices on top of the plastic wrap, arrange them in an even layer, and overlap the pieces slightly. The layer should be large enough to cover the entire tenderloin.
Spread the mushroom mixture evenly over the prosciutto with a spatula.
Lay the seared tenderloin crosswise on the duxelle. Using the plastic wrap, roll the tenderloin up and roll up the sides if necessary to completely enclose the beef. Everything should stay together so the beef tenderloin retains a rectangular shape—place in the fridge for 30 minutes to firm it up.
Preheat oven to 425℉ (220℃).
Flour a board or clean surface. Then, roll out your puff pastry into a rectangle shape. Measure to the pastry is long enough to go all the way around the tenderloin. You may have to seal two sheets together to make it long enough, especially if using premade puff pastry.
Remove the beef from the fridge and carefully remove the plastic wrap. Transfer the tenderloin to the middle of the puff pastry.
Slowly wrap the beef in the puff pastry and cut off any extra pastry ends. Reserve for decorations if desired.
Cut out decorative leaves from the extra pastry. Arrange decoratively on the wrapped beef tenderloin. Place in the refrigerator and let it chill for 10-15 minutes.
Brush the top and sides of the pastry with egg wash, then slit the top of the wrapped beef with a knife to create vents for the steam to be released. Place it on a baking sheet.
Bake for 30-40 minutes until the pastry is golden brown. If the beef is browning too fast, tent with foil. Cooking times will vary depending on the thickness and preferred doneness. An instant-read thermometer will tell you when it reaches the desired temperature. Rare: 115-120°F (46-49°C), medium-rare: 120-125°F (49-52°C), medium: 130 to 135°F (54-57°C), medium-well: 140-145°F (60-63°C), well-done: 150-155°F (66-68°C).
When the beef has reached the desired temperature, remove it from the oven and let it rest for 10-15 minutes before slicing. If you leave it too long without slicing, it might get soggy. Enjoy!