Season the beef tenderloin with half of the sea salt and black pepper on all sides.
Heat olive oil in a heavy skillet over high heat and sear the beef quickly on all sides until browned, then remove immediately to cool.
Finely mince the mushrooms, shallot, and garlic, then sauté them in the same skillet with thyme until all moisture has evaporated and the mixture is concentrated.
Lay a piece of plastic wrap on a flat surface, place the prosciutto slice down, and spread the mushroom duxelles evenly over the prosciutto.
Place the seared beef in the center and use the plastic wrap to roll the prosciutto and mushrooms tightly around the meat, then refrigerate for 15 minutes.
Preheat your oven to 400°F (200°C).
Roll out the puff pastry on a lightly floured surface, unwrap the chilled beef bundle and place it in the center, then fold the pastry over to seal completely.
Place the Wellington on a parchment-lined tray, brush the top with a beaten egg, and bake for 20-25 minutes until the pastry is golden and the beef reaches your desired doneness.