Finely mince the cremini mushrooms and shallot until they reach a paste-like consistency.
Heat olive oil in a skillet over medium heat and sauté the mushroom mixture with fresh thyme until all moisture has evaporated, then season with a pinch of salt and pepper.
Season the beef tenderloin with the remaining salt and pepper, then sear in a very hot pan for 1 minute on all sides to brown the exterior.
Remove the beef from the pan and immediately brush all sides with the Dijon mustard while still warm.
Lay a piece of plastic wrap on a flat surface and arrange the prosciutto slices in a slight overlap.
Spread the mushroom duxelles evenly over the prosciutto, place the beef in the center, and roll it up tightly using the plastic wrap to form a log; chill in the fridge for 15 minutes.
Unroll the chilled beef log onto the puff pastry sheet, wrap it completely while trimming any excess, and brush the surface with a beaten egg wash.
Bake at 400°F for 15 to 20 minutes until the pastry is golden brown and the internal temperature of the beef reaches your desired doneness.