Finely mince the mushrooms and shallots, then sauté in a pan with olive oil until all moisture has evaporated and the mixture is dry.
Season the beef tenderloin with sea salt and black pepper on all sides.
Sear the beef in a very hot pan for about 1 minute per side until browned, then remove and immediately brush with Dijon mustard.
Lay a piece of plastic wrap on a flat surface, arrange the prosciutto slices in an overlapping rectangle, and spread the mushroom duxelles evenly over the ham.
Place the beef in the center and use the plastic wrap to roll the prosciutto and mushrooms tightly around the meat, then chill in the refrigerator for 15 minutes.
Roll out the puff pastry thinly on a floured surface and place the chilled beef bundle in the center.
Fold the pastry over the beef, trimming any excess, and seal the edges using a small amount of beaten egg.
Place the Wellington on a parchment-lined tray, brush the top with the remaining egg wash, and bake at 400°F for 18-20 minutes until the pastry is golden brown.
Allow the beef to rest for at least 5 minutes before slicing into thick rounds to serve.