01 - Preheat oven to 425°F. Pat beef tenderloin dry, season generously with salt and black pepper.
02 - Heat olive oil in a heavy skillet over high heat. Sear beef on all sides until browned, about 2 to 3 minutes per side. Remove and let cool.
03 - In the same skillet, melt butter over medium heat. Add shallots and garlic and sauté until fragrant, about 1 minute. Add mushrooms and thyme, season with salt and pepper; cook, stirring, until moisture evaporates and mixture is dry, about 10 to 12 minutes. Cool completely.
04 - On a sheet of plastic wrap, arrange prosciutto slices slightly overlapping to form a rectangle large enough to wrap the beef. Spread cooled mushroom duxelle evenly over prosciutto.
05 - Brush cooled beef with Dijon mustard. Place beef onto mushroom layer. Using plastic wrap, roll prosciutto and duxelle tightly around beef, seal ends. Wrap tightly and refrigerate for 30 minutes.
06 - Roll out puff pastry on a lightly floured surface to a rectangle large enough to encase the beef. Unwrap beef and place at the center of the pastry. Fold pastry over beef, trim excess, and seal edges. Place seam side down on a parchment-lined baking sheet.
07 - Whisk egg yolk and milk to create egg wash. Brush pastry thoroughly. Chill for 15 minutes to set.
08 - Bake for 40 to 45 minutes until pastry is golden and beef registers 120–125°F for medium-rare. Rest for 10 minutes before slicing.