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 2 minutes per side until a brown crust forms, then remove from heat.
Brush the warm beef immediately with Dijon mustard and set aside to rest.
Finely mince the mushrooms, shallot, and garlic, then sauté in the same skillet with thyme until all liquid has evaporated and the mixture is dry.
Lay a piece of plastic wrap on a flat surface, place the prosciutto slice down, and spread the mushroom duxelles evenly over it.
Place the beef in the center of the mushrooms and use the plastic wrap to roll the prosciutto and mushrooms tightly around the beef into a log shape.
Chill the beef log in the freezer for 10 minutes to firm up.
Roll out the puff pastry thinly, unwrap the chilled beef, and place it in the center of the pastry.
Fold the pastry over the beef to seal it completely, trimming any excess and using a beaten egg to glue the edges.
Place the Wellington on a parchment-lined tray, brush the top with more egg wash, and bake at 400°F for 18 minutes until the pastry is crisp and golden.