01 - Season the beef tenderloin generously with salt and pepper. Heat the olive oil in a large skillet over high heat. Sear the beef on all sides until browned, about 2–3 minutes per side. Remove from heat and let cool slightly. Brush all over with Dijon mustard. Set aside to cool completely.
02 - Melt the butter in a large skillet over medium heat. Add the shallots and garlic; sauté until fragrant, about 1 minute. Add the mushrooms and thyme. Cook, stirring frequently, until the mushrooms release their moisture and the mixture becomes dry and pasty, about 15 minutes. Season with salt and pepper. Let cool completely.
03 - On a large piece of plastic wrap, lay out the prosciutto slices, slightly overlapping, to form a rectangle large enough to wrap the beef. Spread the cooled duxelles evenly over the prosciutto.
04 - Place the cooled beef on top of the mushroom-covered prosciutto. Using the plastic wrap, roll the prosciutto and duxelles around the beef to form a tight log. Twist the ends of the plastic wrap to seal. Refrigerate for 20–30 minutes to firm up.
05 - On a lightly floured surface, roll out the puff pastry to a rectangle large enough to envelop the beef. Remove the beef from the plastic wrap and place it in the center of the pastry.
06 - Brush the edges of the pastry with beaten egg. Fold the pastry over the beef, sealing all edges. Trim any excess pastry if necessary. Place seam-side down on a baking sheet lined with parchment paper. Brush the top with more egg wash. Optionally decorate with extra pastry cutouts.
07 - Chill the wrapped beef in the refrigerator for 15 minutes. Meanwhile, preheat the oven to 425°F.
08 - Bake for 40–45 minutes, or until the pastry is golden brown and an instant-read thermometer inserted into the center of the beef reads 125°F for medium-rare. If the pastry browns too quickly, cover loosely with foil.
09 - Remove from the oven and let rest for 15 minutes before slicing and serving.