Heat olive oil in a skillet over high heat and sear beef on all sides until browned. Remove from skillet and brush with Dijon mustard. Set aside.
In the same skillet, add mushrooms, garlic, and butter. Cook until mushrooms are soft and liquid has evaporated. Season with salt and pepper.
Place prosciutto slices on a sheet of plastic wrap, slightly overlapping. Spread mushroom mixture evenly over prosciutto.
Place beef on top of mushroom mixture and wrap prosciutto tightly around beef. Chill in the refrigerator for 30 minutes.
Roll out puff pastry on a floured surface to about 1/4 inch thickness.
Place beef in the center of the pastry and wrap tightly, sealing edges with beaten egg.
Brush pastry with more beaten egg and bake in a preheated oven at 425°F for 35-40 minutes, or until pastry is golden brown and beef reaches desired doneness.
Let rest for 10 minutes before slicing and serving.
