Finely mince the mushrooms, shallots, and garlic until they form a coarse paste.
Heat olive oil in a skillet over medium heat and sauté the mushroom mixture with thyme until all moisture has evaporated and the mixture is dry.
Season the beef tenderloin with sea salt and black pepper, then sear in a hot pan for 1 minute on all sides to brown; remove and let cool.
Lay a sheet 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, then chill in the fridge for 15 minutes.
Roll out the puff pastry, place the beef roll in the center, and wrap it completely, sealing the edges with a beaten egg wash.
Place the Wellington on a parchment-lined tray, brush the exterior with more egg wash, and bake at 400°F for 20-25 minutes until the pastry is golden and the beef is cooked to your preference.