Finely mince the cremini mushrooms and shallot, then sauté in a dry pan over medium heat with fresh thyme until all moisture has evaporated to create a concentrated duxelles.
Season the beef tenderloin with sea salt and black pepper on all sides.
Heat olive oil in a heavy skillet over high heat and sear the beef for 1 minute per side until a brown crust forms, then remove from heat.
Brush the warm beef immediately with Dijon mustard and let it cool completely in the refrigerator.
Lay a sheet of plastic wrap on a clean surface and arrange the prosciutto slices in an overlapping rectangle.
Spread the mushroom duxelles evenly over the prosciutto, then place the chilled beef in the center.
Use the plastic wrap to roll the prosciutto and mushrooms tightly around the beef, twisting the ends like a candy wrapper, and chill for 20 minutes.
Preheat your oven to 425°F (220°C) and lightly flour a surface to roll out the puff pastry into a thin rectangle.
Unwrap the beef log and place it on the pastry, folding the dough over to seal the edges completely and trimming any excess.
Place the Wellington on a parchment-lined tray, brush the exterior with a beaten egg wash, and bake for 15-20 minutes until the pastry is golden brown.
Remove from the oven and allow the meat to rest for 10 minutes before slicing into thick, elegant rounds.