Season beef with salt and pepper. Heat olive oil in a skillet and sear the beef on all sides. Remove and let cool.
In the same skillet, cook mushrooms until moisture evaporates. Let cool.
Spread plastic wrap on a surface. Lay prosciutto slices, overlapping. Spread mushrooms over prosciutto. Place beef on top and spread mustard over it. Roll up tightly and chill.
Roll out puff pastry. Remove plastic wrap from beef and place in the center of the pastry. Wrap pastry around beef and seal edges. Brush with beaten egg.
Bake for 45 minutes or until pastry is golden brown. Let rest before slicing.