Season the beef tenderloin with sea salt and black pepper, then sear in olive oil over high heat until browned on all sides.
Remove the beef from the pan, let it cool slightly, and brush the entire surface with Dijon mustard.
Finely mince the mushrooms, shallot, and garlic, then sauté in the same pan with thyme until all moisture has evaporated to create a dry duxelles.
Lay out a piece of plastic wrap, place the prosciutto slice on top, spread the mushroom duxelles evenly over the prosciutto, and place the beef in the center.
Roll the beef tightly in the prosciutto and plastic wrap, then chill in the refrigerator for 20 minutes to firm up.
Roll out the puff pastry on a lightly floured surface, unwrap the beef, and place it in the center of the pastry.
Fold the pastry over the beef, trim any excess, seal the edges with a bit of egg wash, and brush the entire exterior with the remaining beaten egg.
Bake at 425°F for 15-20 minutes until the pastry is golden brown and the beef reaches an internal temperature of 125°F for medium-rare.
Allow the Wellington to rest for 10 minutes before slicing into thick portions.