Preheat oven to 425°F (220°C). Season the beef tenderloin generously with salt and black pepper.

Heat olive oil in a skillet over high heat. Sear the beef on all sides until browned, about 2-3 minutes per side. Remove and let cool, then brush with Dijon mustard.

In the same skillet, melt butter over medium heat. Add mushrooms, garlic, and thyme. Cook until mushrooms release their moisture and become a thick paste (duxelles), about 10 minutes. Let cool.

Lay out a sheet of plastic wrap. Arrange prosciutto slices in an overlapping layer. Spread the mushroom duxelles evenly over the prosciutto.

Place the seared beef in the center of the prosciutto-mushroom layer. Using the plastic wrap, tightly roll the prosciutto and mushrooms around the beef. Chill in the fridge for 15 minutes.

Roll out the puff pastry on a floured surface. Unwrap the beef and place it in the center of the pastry. Fold the pastry over the beef, sealing the edges with egg wash. Trim excess pastry if needed.

Place the wrapped beef seam-side down on a baking sheet. Brush the pastry with egg wash. Optionally, score the top lightly with a knife for decoration.

Bake for 25-30 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.