Prepare the Beef: Season the beef tenderloin generously with salt and pepper. Heat olive oil in a skillet over high heat, and sear the beef on all sides until browned (about 2-3 minutes per side). Remove from heat and let cool. Brush with Dijon mustard.

Make the Mushroom Duxelles: In the same skillet, add chopped mushrooms and cook over medium heat until the moisture evaporates and the mushrooms are golden brown. Season with salt, pepper, and thyme. Let cool.

Wrap with Prosciutto: Lay out slices of prosciutto on a sheet of plastic wrap, slightly overlapping. Spread the mushroom mixture over the prosciutto, then place the beef on top. Using the plastic wrap, roll tightly to form a log. Chill in the refrigerator for 15-20 minutes.

Assemble with Puff Pastry: Preheat the oven to 400°F (200°C). Roll out the puff pastry on a floured surface. Unwrap the beef from the plastic wrap and place it in the center of the pastry. Fold the pastry over the beef, sealing the edges. Brush the pastry with beaten egg.

Bake: Place the wrapped beef on a baking sheet. Bake for 30-35 minutes, or until the pastry is golden brown and the internal temperature of the beef reaches 125°F (52°C) for medium-rare. Let rest for 10 minutes before slicing.