01 - Preheat oven to 400°F. Season beef with salt and pepper. Heat olive oil in a large skillet over high heat and sear beef on all sides until browned, approximately 2 minutes per side. Remove and allow to cool.
02 - Melt butter in the same skillet over medium heat. Add shallots and garlic, sauté for 2 minutes. Incorporate mushrooms and thyme, cooking until mushrooms release moisture and mixture is dry, about 10 minutes. Season with salt and pepper and let cool completely.
03 - On a large sheet of plastic wrap, arrange prosciutto slices overlapping to form a rectangle large enough to wrap the beef. Spread mushroom duxelles evenly over the prosciutto.
04 - Brush cooled beef with Dijon mustard and place it on the mushroom-covered prosciutto. Using the plastic wrap, roll tightly to encase the beef. Twist ends to seal and refrigerate for 20 minutes.
05 - Roll out puff pastry on a lightly floured surface to a rectangle large enough to enclose the beef. Unwrap the beef and position it in the center of the pastry. Fold pastry over the beef, trim excess, and seal edges. Place seam-side down on a parchment-lined baking sheet.
06 - Beat egg yolk with milk and brush evenly over the pastry. Lightly score the top with a sharp knife for decoration.
07 - Bake for 40 to 45 minutes until pastry is golden and internal beef temperature reaches 120–125°F for medium-rare. Let rest for 10 minutes before slicing.