Season beef fillet generously with salt and pepper. Sear all sides in hot oil until browned (about 2 minutes total). Let cool completely, then refrigerate for 30 minutes.

Finely chop mushrooms and cook in butter over high heat until all moisture evaporates and mushrooms are golden brown. Process into a paste (duxelles). Add thyme and season.

Roll out puff pastry into a rectangle large enough to wrap the beef. Spread prosciutto slices on pastry, then spread mushroom duxelles over prosciutto.

Brush beef with Dijon mustard and place in center of pastry. Fold pastry over beef, trimming excess. Seal edges with beaten egg. Refrigerate 30 minutes.

Brush with egg wash and make decorative slits on top. Bake at 200°C (400°F) for 30-35 minutes until pastry is golden and internal temperature reaches 52°C (125°F) for medium-rare. Rest 10 minutes before slicing.