Preheat oven to 200°C/400°F. Heat oil in a large skillet over high heat. Season beef with salt and pepper, sear on all sides until browned. Let cool and brush with mustard.
In the same skillet, melt butter and add mushrooms, shallots, and garlic. Cook until moisture evaporates and mixture is dry.
Lay out prosciutto slices on a sheet of plastic wrap, slightly overlapping. Spread mushroom mixture over prosciutto. Place beef on top and roll up tightly. Chill for 15 minutes.
Roll out puff pastry and place beef in the center. Fold over pastry to enclose beef completely. Brush with beaten egg.
Place on a baking sheet and bake for 40-45 minutes, until pastry is golden and beef reaches desired doneness. Let rest for 10 minutes before slicing.
Prep Time: 30 min | Total Time: 1 hr 45 min | Servings: 6