Preheat your oven to 400°F (200°C).
Season the beef tenderloin with sea salt and black pepper on all sides.
Heat olive oil in a cast-iron skillet over high heat and sear the beef for 1-2 minutes per side until browned, then remove and immediately brush with Dijon mustard.
Finely mince the mushrooms, shallot, and garlic, then sauté them in the same skillet with thyme until all moisture has evaporated and the mixture is dry.
Lay a sheet of plastic wrap on a flat surface and arrange the prosciutto slices in an overlapping rectangle.
Spread the mushroom duxelles evenly over the prosciutto, place the beef in the center, and roll it up tightly using the plastic wrap; chill in the fridge for 15 minutes.
Roll out the puff pastry thinly, remove the plastic from the beef, and place the beef in the center of the pastry.
Fold the pastry over the beef, trimming any excess, and seal the edges with a beaten egg wash.
Place the Wellington on a parchment-lined baking sheet, brush the entire exterior with egg wash, and bake for 20-25 minutes until the pastry is golden brown and the beef reaches an internal temperature of 130°F for medium-rare.
Let the roast rest for 10 minutes before slicing into thick rounds.