Season the beef tenderloin with sea salt and black pepper on all sides.
Heat olive oil in a skillet over high heat and sear the beef for 1 minute per side until browned but rare in the middle; remove and let cool completely.
Finely mince the cremini mushrooms and sauté them in the same skillet with fresh thyme until all moisture has evaporated and they form a thick paste.
Lay out a piece of plastic wrap, place the prosciutto slices on top, and spread the mushroom duxelles evenly over the prosciutto.
Brush the cooled beef with Dijon mustard and place it in the center of the mushroom-covered prosciutto.
Use the plastic wrap to tightly roll the prosciutto and mushrooms around the beef, then chill in the refrigerator for 15 minutes to set the shape.
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 to seal it completely, trimming any excess, and place seam-side down on a parchment-lined baking sheet.
Brush the pastry with a beaten egg wash and bake at 425°F for 15-20 minutes until the pastry is crisp and golden brown.
Let the Wellington rest for 5 minutes before slicing into thick, succulent rounds.