Finely mince the mushrooms, shallot, and garlic until they reach a paste-like consistency.
Sauté the mushroom mixture in a dry pan over medium heat until all moisture has evaporated, then stir in the fresh thyme and a pinch of salt.
Season the beef tenderloin with sea salt and black pepper, then sear in olive oil over high heat for 60 seconds per side until browned but rare inside.
Remove the beef from the pan and immediately brush all sides with the Dijon mustard while the meat is still warm.
Lay out a piece of plastic wrap and place the prosciutto slice on it, followed by an even layer of the 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 the puff pastry out into a thin rectangle on a lightly floured surface.
Unwrap the chilled beef, place it on the pastry, and wrap the pastry around it, trimming any excess and sealing the edges with a bit of beaten egg.
Place the Wellington on a parchment-lined tray, brush the exterior with the remaining egg wash, and score the top lightly with a knife.
Bake at 425°F for 15 to 20 minutes until the pastry is deeply golden and the internal temperature of the beef reaches 125°F for medium-rare.