Season the beef tenderloin with half of the sea salt and black pepper.
Heat olive oil in a skillet over high heat and sear the beef on all sides until a brown crust forms, then remove and let cool.
Finely mince the mushrooms, shallot, and garlic, then sauté in the same skillet until all moisture has evaporated.
Stir in the fresh thyme and let the mushroom duxelles cool completely.
Lay a piece of plastic wrap on a flat surface and overlap the prosciutto slices on top to form a rectangle.
Spread the cooled mushroom duxelles over the prosciutto, then place the beef in the center and roll tightly using the plastic wrap.
Chill the beef roll in the refrigerator for 15 minutes to help it hold its shape.
Roll the puff pastry into a thin sheet, wrap it around the chilled beef bundle, and seal the edges with a bit of egg wash.
Brush the entire pastry with the remaining beaten egg, sprinkle with the rest of the salt and pepper, and bake at 400°F for 20 minutes until golden and crisp.