Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.

In a frying pan, heat the olive oil over medium heat. Add the finely chopped mushrooms and season with salt and pepper. Sauté for about 7-10 minutes until the mushrooms are cooked down and any liquid has evaporated. Remove from heat and let cool.

While the mushrooms are cooling, season the beef tenderloin with salt and pepper. In the same frying pan, sear the beef on all sides for about 2 minutes per side until browned. Remove from heat and brush all sides with Dijon mustard. Allow to cool slightly.

Lay out the prosciutto slices on a piece of plastic wrap, slightly overlapping. Spread the cooled mushroom mixture evenly over the prosciutto.

Place the seared beef in the center and wrap it tightly using the plastic wrap, forming a log. Chill in the refrigerator for 15 minutes.

Roll out the puff pastry on a lightly floured surface into a rectangle large enough to cover the beef completely. Remove the beef from the plastic wrap and place it in the center of the pastry.

Carefully fold the pastry over the beef, sealing the edges with a fork or by pinching them together. Cut any excess pastry and tuck the ends under.

Brush the pastry with the beaten egg to give it a golden finish. Make a few slits on top for steam to escape.

Place the wrapped beef on the prepared baking sheet and bake in the preheated oven for 25-30 minutes until the pastry is golden brown and crisp. Use a meat thermometer to check that the internal temperature of the beef reaches 135°F (57°C) for medium-rare.

Allow the Beef Wellington to rest for 10 minutes before cutting and serving.