Finely mince the cremini mushrooms, shallots, and garlic until they reach a paste-like consistency.
Sauté the mushroom mixture in a dry pan over medium heat with fresh thyme until all moisture has evaporated and the mixture is browned.
Season the beef tenderloin with sea salt and black pepper, then sear in olive oil over high heat for 1 minute per side until a crust forms.
Brush the warm beef tenderloin on all sides with Dijon mustard and set aside to rest.
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 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, unwrap the beef, and place it in the center of the pastry.
Fold the pastry over the beef, trimming any excess, and seal the edges using a small amount of beaten egg.
Place the Wellington on a parchment-lined baking sheet, brush the entire exterior with the remaining egg wash, and bake at 400°F for 15-20 minutes until the pastry is golden brown.