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 until browned on all surfaces, then remove and brush with Dijon mustard while warm.
Finely mince the mushrooms, shallots, and garlic, then sauté them in the same skillet with thyme until all moisture has evaporated and the mixture is dry.
Lay a piece of plastic wrap on a flat surface and overlap the prosciutto slices to form a rectangle.
Spread the mushroom duxelles evenly over the prosciutto, then place the beef in the center.
Use the plastic wrap to roll the prosciutto and mushrooms tightly around the beef into a log, then chill in the refrigerator for 20 minutes.
Roll out the puff pastry and wrap it around the chilled beef log, trimming any excess and sealing the seams with a bit of egg wash.
Place the Wellington on a baking sheet, brush the exterior with the remaining egg wash, and bake at 400°F for 20-25 minutes until the pastry is golden brown.