01 - Preheat oven to 425°F. Pat beef tenderloin dry and season generously with salt and pepper.
02 - Heat olive oil in a heavy skillet over high heat. Sear beef on all sides until browned, approximately 2 to 3 minutes per side. Remove from heat 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, and cook, stirring occasionally, until the mixture is dry and moisture evaporates, about 10 to 12 minutes. Remove from heat and allow to cool completely.
04 - On a sheet of plastic wrap, lay out the prosciutto slices, slightly overlapping to form a rectangle large enough to wrap the beef. Spread the cooled mushroom duxelle evenly over the prosciutto.
05 - Brush the cooled beef with Dijon mustard. Place beef on the mushroom layer. Use plastic wrap to tightly roll prosciutto and duxelle around the beef, sealing the ends. Wrap tightly and chill for 30 minutes.
06 - Roll out the puff pastry on a lightly floured surface to a rectangle large enough to encase the beef completely. Unwrap the chilled beef and place it in the center of the pastry. Fold pastry over the beef, trim excess, and seal edges firmly. Transfer with seam side down onto a parchment-lined baking sheet.
07 - Whisk together egg yolk and milk to make an egg wash. Brush the entire pastry surface evenly. Chill for 15 minutes to set.
08 - Bake in the preheated oven for 40 to 45 minutes, or until the pastry is golden brown and beef registers 120–125°F for medium-rare doneness. Remove and rest for 10 minutes before slicing.