Season the beef tenderloin with sea salt and black pepper on all sides.
Heat olive oil in a pan over high heat and sear the beef for 1 minute per side until browned; remove and let cool completely.
Finely mince the mushrooms, shallot, and garlic, then sauté in the same pan with fresh thyme until all moisture has evaporated and the mixture is dry.
Once the beef is cool, brush all sides evenly with the Dijon mustard.
Lay a piece of plastic wrap on a flat surface, place the prosciutto slice down, spread the mushroom duxelles over it, and place the 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 on a lightly floured surface, unwrap the beef bundle, and place it in the center of the pastry.
Fold the pastry over the beef, sealing the edges with a bit of the beaten egg wash, and place seam-side down on a baking sheet.
Brush the entire pastry with the remaining egg wash and bake at 400°F for 20-25 minutes until the pastry is golden and the beef reaches an internal temperature of 130°F.
Let the Wellington rest for 10 minutes before slicing into thick rounds.