Preheat your oven to 400°F (200°C) and line a small baking sheet with parchment paper.
Finely mince the mushrooms, shallots, and garlic until they reach a paste-like consistency.
Sauté the mushroom mixture and thyme in a dry skillet over medium heat for 8-10 minutes until all moisture has evaporated, then set aside to cool completely.
Season the beef tenderloin with sea salt and black pepper on all sides.
Heat olive oil in a heavy skillet over high heat and sear the beef for 1 minute per side to develop a crust, then remove and immediately brush with Dijon mustard.
Lay a piece of plastic wrap on a clean surface and place the prosciutto slice on top, followed by an even layer of the cooled mushroom duxelles.
Place the beef in the center and use the plastic wrap to roll the prosciutto and mushrooms tightly around the meat, then chill in the freezer for 10 minutes.
Roll out the puff pastry on a lightly floured surface, place the chilled beef bundle in the center, and wrap the pastry around it, sealing the edges with a bit of water.
Place the Wellington on the baking sheet, brush the pastry with the beaten egg wash, and bake for 20-25 minutes until the pastry is golden brown and the beef reaches your desired doneness.
Allow the beef to rest for 5-10 minutes before slicing with a serrated knife.