01 - Preheat oven to 425°F. Season the beef tenderloin generously with salt and pepper.
02 - Heat olive oil in a heavy skillet over high heat. Sear the beef on all sides until browned, about 2 minutes per side. Remove and let cool; brush all sides with Dijon mustard.
03 - Melt butter in a skillet over medium heat. Add shallots and garlic; sauté until fragrant. Add mushrooms and thyme, season with salt and pepper, and cook, stirring often, until mushrooms release their moisture and mixture becomes dry and paste-like, about 10–15 minutes. Cool completely.
04 - Lay a large piece of plastic wrap on a work surface. Arrange the prosciutto slices side by side, slightly overlapping, to form a rectangle large enough to wrap the beef.
05 - Spread the cooled mushroom duxelles evenly over the prosciutto. Place the beef on top and, using the plastic wrap, roll the prosciutto and duxelles around the beef into a tight log. Twist the ends of the plastic wrap to secure. Chill for 30 minutes.
06 - On a lightly floured surface, roll out the puff pastry into a rectangle large enough to wrap the beef. Remove beef from plastic wrap and place in the center of the pastry.
07 - Fold the pastry over the beef, trimming excess if needed, and seal the edges. Place seam-side down on a parchment-lined baking sheet. Brush with egg wash.
08 - Chill in the refrigerator for 15 minutes. Brush with a second layer of egg wash and, if desired, score the pastry lightly with a sharp knife for decoration.
09 - Bake for 40–45 minutes, or until pastry is golden and an instant-read thermometer inserted into the center of the beef registers 120°F for rare, 130°F for medium-rare.
10 - Let rest for 15 minutes before slicing and serving.