Season the beef tenderloin fillet on all sides with sea salt and black pepper.
Heat olive oil in a skillet over high heat and sear the beef for 1 minute per side until browned, then remove and immediately brush with Dijon mustard.
Finely mince the mushrooms, shallot, and garlic, then sauté them in the same skillet until all moisture has evaporated and the mixture forms a thick paste.
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, roll the prosciutto and mushrooms tightly around the beef using the plastic wrap, and chill in the refrigerator for 15 minutes.
Roll out the puff pastry thinly, remove the plastic wrap from the beef, and wrap the pastry around the beef bundle, sealing the edges with a bit of water.
Place the Wellington on a baking sheet, brush the exterior with a beaten egg wash, and bake at 400°F for 20-25 minutes until the pastry is golden brown.