- Preheat your oven to 400°F. 
- Heat olive oil and butter in a large pan over high heat. 
- Season the beef fillet generously with salt and black pepper. 
- Sear in the hot pan for about 4 minutes, turning to seal all sides, then remove and let rest. 
- In the same pan, lower the heat to medium and add the chopped mushrooms and rosemary. 
- Cook until mushrooms are soft and any liquid has evaporated. 
- Remove from heat and let them cool. 
- Place a sheet of plastic wrap on a flat surface and lay prosciutto slices in a single layer. 
- Spread the cooled mushroom mixture over the prosciutto. 
- Brush the cooled beef fillet with Dijon mustard and place on the prosciutto layer. 
- Wrap it tightly with the plastic wrap and refrigerate for 15 minutes. 
- Roll out the puff pastry, remove the beef from the plastic wrap, and lay it on the pastry. 
- Fold the pastry over the beef, sealing the edges with a little water. 
- Transfer the wrapped beef to a baking tray seam-side down. 
- Beat the egg and brush over the pastry for a nice glaze. 
- Bake for 20-25 minutes until the pastry is golden and flaky.