01 - Season the beef generously with salt and pepper. Heat vegetable oil in a large skillet over high heat. Sear beef on all sides until browned, about 2-3 minutes per side. Remove and let cool completely.
02 - In the same pan, melt butter over medium heat. Add shallots and garlic; sauté until softened, about 2 minutes. Add mushrooms and thyme. Cook, stirring often, until mushrooms release moisture and mixture becomes dry and pasty, about 10-15 minutes. Season with salt and pepper. Set aside to cool.
03 - Lay a large sheet of plastic wrap on work surface. Arrange prosciutto slices in slightly overlapping layer to form rectangle large enough to wrap beef.
04 - Spread cooled mushroom duxelles evenly over prosciutto. Place cooled beef on top. Using plastic wrap, roll prosciutto and mushroom mixture tightly around beef to form log. Twist ends of wrap to secure. Chill in refrigerator for at least 30 minutes.
05 - Roll out puff pastry on floured surface to rectangle large enough to completely enclose beef. Unwrap beef log and place in center of pastry.
06 - Mix egg yolk with milk to make egg wash. Brush edges of pastry with egg wash. Fold pastry over beef, sealing edges tightly. Trim excess pastry if needed. Place seam-side down on baking sheet lined with parchment.
07 - Brush top with egg wash. Use remaining pastry to decorate if desired. Chill in refrigerator for 15 minutes. Preheat oven to 425°F.
08 - Bake for 40-45 minutes, or until pastry is golden and meat thermometer inserted into center reads 122°F for medium-rare. Rest for 15 minutes before slicing.
09 - Serve with Dijon mustard if desired.