Preheat oven to 400°F and finely mince the mushrooms and shallot.
Sauté mushrooms, shallot, and thyme in ghee until all moisture evaporates, then season with sea salt and black pepper.
Season the beef with sea salt and black pepper, then sear in a hot pan for 1-2 minutes per side until browned but raw inside.
Brush the seared beef with Dijon mustard and let it rest briefly.
Lay out a piece of plastic wrap, place the prosciutto slice on it, spread the mushroom mixture over the prosciutto, and place the beef in the center.
Roll the beef tightly in the prosciutto and mushrooms using the plastic wrap and chill for 15 minutes to set the shape.
Roll out the puff pastry thinly, remove the plastic from the beef, and wrap the pastry around the beef bundle, sealing the edges.
Brush the pastry with a beaten egg wash and bake for 15-20 minutes until the pastry is golden brown and beef reaches desired doneness.