Season the beef tenderloin with sea salt and black pepper, then sear in a hot skillet with ghee until browned on all sides.
Remove the beef from the skillet and immediately brush with Dijon mustard, allowing it to cool completely.
Pulse mushrooms, shallot, garlic, and thyme in a food processor until finely minced, then sauté in the same skillet until all liquid has evaporated.
Place a layer of plastic wrap on a flat surface, lay the prosciutto slice down, spread the mushroom mixture evenly over it, and place the beef in the center.
Roll the prosciutto and mushrooms tightly around the beef using the plastic wrap, then chill in the refrigerator for 20 minutes to set the shape.
Wrap the chilled beef bundle in the puff pastry, brush with the beaten egg, and bake at 400°F until the pastry is golden and the beef reaches your desired doneness.