01 - Set the oven to 425°F.
02 - Generously season the beef tenderloin with salt and freshly ground black pepper.
03 - Heat olive oil in a heavy skillet over high heat. Sear the beef on all sides until evenly browned, approximately 2 to 3 minutes per side. Transfer to a plate and allow to cool completely.
04 - In the same skillet, melt unsalted butter over medium heat. Add minced shallots and cook until translucent. Stir in garlic, chopped mushrooms, fresh thyme, salt, and pepper. Sauté, stirring frequently, until the mixture is dry and all moisture has evaporated, about 8 to 10 minutes. Remove from heat and let cool completely.
05 - Lay a large sheet of plastic wrap on the workspace. Arrange prosciutto slices in a slightly overlapping rectangle sufficient to wrap the beef. Spread the cooled mushroom duxelle evenly over the prosciutto.
06 - Brush the cooled beef tenderloin with Dijon mustard. Position it on the mushroom-covered prosciutto. Using the plastic wrap, roll the prosciutto and duxelle tightly around the beef, sealing securely. Twist the ends of the plastic wrap and refrigerate for 30 minutes.
07 - On a lightly floured surface, roll out the puff pastry into a rectangle large enough to encase the beef. Unwrap the chilled beef and place it in the center of the pastry.
08 - Brush the edges of the pastry with beaten egg. Fold pastry over the beef, trimming excess if necessary, and seal the edges thoroughly. Place the parcel seam-side down on a parchment-lined baking sheet. Brush the top with additional egg wash. Optionally, lightly score the pastry for decoration.
09 - Bake in the preheated oven for 40 to 45 minutes, until the pastry is golden brown and a meat thermometer inserted into the center registers 120–125°F for medium rare.
10 - Allow the beef wellington to rest for 10 to 15 minutes before slicing and serving.