Finely mince the mushrooms, shallots, and garlic, then sauté in a dry pan over medium heat until all moisture evaporates to create a thick, concentrated duxelles.
Season the beef tenderloin with the sea salt and black pepper, then sear in a hot pan with olive oil for 1 minute per side until a brown crust forms.
Remove the beef from the pan and immediately brush with Dijon mustard while warm, then set aside to rest.
Lay a sheet of plastic wrap on a clean surface, place the prosciutto slice down, and spread the mushroom duxelles evenly over the prosciutto.
Place the beef in the center and use the plastic wrap to roll the prosciutto and mushrooms tightly around the meat, chilling in the refrigerator for 15 minutes to set.
Roll out the puff pastry, unwrap the chilled beef, and place it in the center of the pastry; fold the pastry over the beef, trimming any excess and sealing the edges with a bit of water.
Brush the entire exterior of the pastry with a beaten egg wash and bake at 425°F (220°C) for 15-20 minutes until the pastry is golden brown and the internal temperature of the beef reaches your desired level.