Finely mince the mushrooms and garlic, then sauté in olive oil over medium heat until all moisture has evaporated to create a concentrated duxelles.
Season the beef tenderloin with sea salt and black pepper, then sear in a hot pan on all sides until browned but still raw in the center.
Brush the warm beef tenderloin immediately with Dijon mustard and set aside to cool.
Lay a sheet of plastic wrap on a flat surface, arrange the prosciutto slices in an overlapping rectangle, and spread the mushroom duxelles evenly over the top.
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 20 minutes.
Roll out the puff pastry on a lightly floured surface, unwrap the chilled beef bundle, and place it in the center of the pastry.
Fold the pastry over the beef to seal it completely, brushing the edges with a beaten egg to act as glue, then place seam-side down on a baking sheet.
Brush the entire exterior with egg wash, score the top lightly with a knife, and bake at 400°F for 20-25 minutes until the pastry is golden and the beef reaches an internal temperature of 125°F.
Allow the Wellington to rest for at least 10 minutes before slicing into thick, succulent portions.