Preheat your oven to 425°F (220°C) and line a baking sheet with parchment paper.
Season the beef tenderloin with sea salt and black pepper, then sear in olive oil over high heat for 2 minutes per side until a brown crust forms; remove and let cool completely.
Finely mince the mushrooms and shallots, then sauté them in the same pan with fresh thyme until all moisture has evaporated and the mixture becomes a thick paste.
Lay out a piece of plastic wrap, place the prosciutto slices slightly overlapping, and spread the mushroom duxelles evenly over the prosciutto.
Place the seared beef in the center, roll it tightly using the plastic wrap to form a uniform log, and chill in the refrigerator for 15 minutes to firm up.
Roll out the puff pastry on a lightly floured surface, remove the plastic from the beef, place the beef on the pastry, and fold the edges to seal it completely.
Brush the pastry with the beaten egg wash, place it on the prepared baking sheet, and bake for 15-20 minutes until the pastry is golden and the beef reaches an internal temperature of 130°F for medium-rare.