01 - Preheat the oven to 425°F. Pat beef dry and season generously with salt and black pepper.
02 - Heat olive oil in a large skillet over high heat. Sear the beef on all sides until well browned, about 2 to 3 minutes per side. Remove from heat, let cool, then brush all over with Dijon mustard.
03 - Melt butter in a skillet over medium heat. Add shallots and garlic and sauté until fragrant, approximately 2 minutes. Add mushrooms and thyme; cook, stirring frequently, until the mixture is paste-like and moisture evaporates, 10 to 15 minutes. Season with salt and pepper. Cool completely.
04 - Lay plastic wrap on a work surface. Arrange prosciutto slices in an overlapping layer to form a rectangle sufficient to wrap the beef. Spread cooled mushroom duxelles evenly over prosciutto. Place beef fillet atop duxelles.
05 - Using plastic wrap, roll prosciutto and duxelles tightly around beef, forming a log. Twist ends to seal. Refrigerate for 30 minutes.
06 - On a lightly floured surface, roll puff pastry into a rectangle large enough to enclose the beef. Unwrap beef from plastic wrap and place in center of pastry.
07 - Fold pastry over beef, trimming excess and pressing to seal seams. Place seam-side down on a parchment-lined baking sheet.
08 - Whisk egg yolk with milk to create egg wash. Brush pastry surface evenly. Decorate with pastry scraps if desired.
09 - Bake for 40 to 45 minutes, or until pastry is golden brown and an instant-read thermometer inserted into center of beef registers 120–125°F for medium-rare.
10 - Allow to rest for 10 to 15 minutes before slicing and serving.