Finely mince the cremini mushrooms and shallots until they resemble a coarse paste.
Sauté the mushroom mixture and thyme in a dry pan over medium heat until all liquid has evaporated, then set aside to cool.
Season the beef tenderloin with sea salt and black pepper, then sear in olive oil over high heat for 1 minute per side until browned but raw in the middle.
Lay a piece of plastic wrap on a flat surface, place the prosciutto slice down, and spread the cooled mushroom duxelles evenly over it.
Place the seared beef in the center and use the plastic wrap to roll the prosciutto and mushrooms tightly around the meat; chill in the refrigerator for 15 minutes.
Roll out the puff pastry thinly on a floured surface, remove the plastic from the beef, and wrap the pastry around the beef bundle, sealing the seams with a little water.
Place the Wellington on a baking sheet, brush the exterior with a beaten egg, and bake at 400°F (200°C) for 15-20 minutes until the pastry is golden brown.