Heat olive oil in a skillet over high heat. Sear the beef tenderloin on all sides until browned. Remove from heat and let cool.
In the same skillet, cook the mushrooms until they release their moisture and become dry. Let cool.
Brush the beef with Dijon mustard.
Lay out a layer of plastic wrap. Place the prosciutto slices on the plastic wrap, overlapping slightly. Spread the mushrooms over the prosciutto. Place the beef on top and roll it up tightly using the plastic wrap. Chill in the refrigerator for 15 minutes.
Roll out the puff pastry on a floured surface. Remove the beef from the plastic wrap and place it in the center of the pastry. Fold the pastry over the beef and seal the edges. Brush with beaten egg.
Place the wrapped beef on a baking sheet. Bake for 25-30 minutes or until the pastry is golden brown. Let rest for 10 minutes before slicing.