Preheat your oven to 400°F and line a small baking sheet with parchment paper.
Finely mince the cremini mushrooms and shallot, then sauté them in olive oil over medium heat 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 skillet for 2 minutes per side until a brown crust forms.
Remove the beef from the pan and immediately brush all sides with Dijon mustard, then let it rest for 5 minutes.
Lay the prosciutto on a piece of plastic wrap, spread the mushroom mixture evenly over it, and wrap it tightly around the beef fillet.
Roll out the puff pastry on a lightly floured surface, place the beef bundle in the center, wrap it tightly, and trim any excess dough.
Place the Wellington on the baking sheet, brush the top with a beaten egg wash, and bake for 20-25 minutes until the pastry is crisp and golden.