Season the beef tenderloin generously with salt and pepper. Sear the beef in hot olive oil in a skillet on all sides until deeply browned, about 1 minute per side. Remove the beef and brush all over with Dijon mustard while it is still warm. Let it cool completely.
Prepare the duxelles: Pulse the mushrooms and shallots in a food processor until very finely chopped. Cook the mixture in a dry skillet over medium heat, stirring often, until all the moisture has evaporated (about 15-20 minutes). Add butter, thyme, and cook for 1 minute. Deglaze with white wine and cook until evaporated. Stir in brandy, if using. Spread the duxelles on a plate to cool completely.
Place the cooled beef tenderloin at the edge of the prosciutto/duxelles layer. Use the plastic wrap to tightly roll the prosciutto and duxelles around the beef. Twist the ends of the plastic wrap tightly to form a compact log. Refrigerate for at least 30 minutes to firm up.
Lightly dust your work surface with flour. Roll out the puff pastry into a rectangle large enough to completely enclose the beef log. Remove the plastic wrap from the beef log and place it on the pastry. Brush the edges of the pastry with egg wash.
Wrap the pastry tightly around the beef, trimming any excess dough. Seal the seams well. Place the Wellington seam-side down on a baking sheet lined with parchment paper. Brush the entire surface with egg wash. Chill for another 15 minutes.
Preheat your oven to 400 degrees F (200 degrees C). Brush the pastry one more time with egg wash. Score the top lightly with the back of a knife in a decorative pattern, avoiding cutting through to the meat.
Bake for 25 to 35 minutes, depending on your desired doneness. For medium-rare, aim for an internal temperature of 125 degrees F (52 degrees C). Use a meat thermometer inserted through the pastry into the center of the beef.
Let the Beef Wellington rest for 10 minutes before slicing into thick portions. Serve immediately.
Notes
For a crispier bottom crust, you can place the wrapped Wellington on a preheated baking stone or steel for the first 15 minutes of baking.
If you are planning your meal prep, consider using a sous-vide precision cooker to perfectly cook the beef before searing and wrapping.
If you are trying to manage your diet, this recipe is rich; consider pairing it with light, fresh vegetables instead of heavy sides.