01 - Preheat oven to 425°F. Season the beef tenderloin generously with salt and pepper. Heat olive oil in a heavy skillet over high heat. Sear the beef on all sides until browned, about 2 minutes per side. Remove from heat and let cool completely, then brush all surfaces with Dijon mustard.
02 - 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 frequently, until mushrooms release their moisture and the mixture becomes dry and paste-like, 10 to 15 minutes. Cool completely before proceeding.
03 - Lay a large sheet of plastic wrap on a work surface. Arrange prosciutto slices side by side, slightly overlapping, to create a rectangle large enough to encase the beef. Spread cooled mushroom duxelles evenly over the prosciutto. Place the seared beef on top and, using the plastic wrap, roll the prosciutto and duxelles around the beef into a tight cylinder. Twist the ends of the plastic wrap to secure. Refrigerate for 30 minutes.
04 - On a lightly floured surface, roll out puff pastry into a rectangle large enough to wrap the beef completely. Remove beef from plastic wrap and place in the center of the pastry. Fold the pastry over the beef, trimming any excess, and seal the edges thoroughly. Place seam-side down on a parchment-lined baking sheet. Brush with egg wash.
05 - Refrigerate for 15 minutes. Brush with a second layer of egg wash. If desired, score the pastry lightly with a sharp knife for decorative patterning.
06 - Bake for 40 to 45 minutes, until pastry is deep golden and an instant-read thermometer inserted into the center registers 120°F for rare or 130°F for medium-rare. Transfer to a cutting board and rest for 15 minutes before slicing into thick medallions and serving.