Preheat your oven to 400°F (200°C) and line a small baking sheet with parchment paper.
Season the beef tenderloin on all sides with sea salt and black pepper.
Heat olive oil in a heavy skillet over high heat and sear the beef for 2 minutes per side until a brown crust forms, then remove from heat.
Immediately brush the warm beef on all sides with the Dijon mustard and set aside to rest.
Finely mince the cremini mushrooms and sauté them with fresh thyme in the same skillet until all liquid has evaporated and they form a thick paste.
Lay a sheet of plastic wrap on a clean surface, place the prosciutto slice down, and spread the mushroom paste evenly over the prosciutto.
Place the beef in the center, roll the prosciutto and mushrooms tightly around the beef using the plastic wrap, and chill in the freezer for 10 minutes to firm up.
Roll out the puff pastry, wrap it tightly around the chilled beef log, and seal the edges by brushing with a little beaten egg.
Place the Wellington on the baking sheet, brush the entire pastry with the remaining egg wash, and bake for 20-25 minutes until the pastry is golden and crisp.