Preheat the oven to 400°F (200°C).

Season the beef tenderloin with salt and pepper. In a skillet, heat olive oil over medium-high heat and sear the beef on all sides until browned (about 2-3 minutes per side). Remove from heat, brush the tenderloin with Dijon mustard, and let it cool.

In the same skillet, add the chopped onions and garlic. Sauté until translucent. Add the finely chopped mushrooms and thyme, cooking until all moisture is evaporated (around 5-7 minutes). Season with salt and pepper, then remove from heat and allow to cool.

On a clean surface, lay out the prosciutto slices in an overlapping manner. Spread the cooled mushroom mixture over the prosciutto.

Place the seasoned beef in the center and carefully wrap the prosciutto around it. Use plastic wrap to tightly wrap the beef and refrigerate for 15 minutes.

Roll out the puff pastry on a lightly floured surface to a size that can fully enclose the beef.

Remove the beef from the plastic wrap, place it in the center of the pastry, and fold the pastry over it. Seal the edges by pinching them closed. Brush the top with the beaten egg.

Place the wrapped beef Wellington on a baking tray lined with parchment paper. Make a few small slits in the pastry to allow steam to escape.

Bake in the preheated oven for 20-25 minutes, or until the pastry is golden brown and a meat thermometer inserted into the center reads 130°F (54°C) for medium-rare.

Let the Beef Wellington rest for 10 minutes before slicing. Serve warm.