Pat the beef tenderloin dry with paper towels. Then, season the fillet generously with salt and pepper.
Heat olive oil in a large, heavy skillet over high heat. Sear the fillet on all sides, including the ends, about 2-3 minutes until evenly browned. Remove the fillet from the pan and transfer to a plate to cool.
While the fillet cools, prepare the mushroom duxelles. Wash and dry the mushrooms. Peel both the shallots and garlic. Add mushrooms, shallots, and garlic to a food processor and pulse until finely chopped.
Heat the same heavy skillet used to sear the fillet over medium-high heat. Transfer the mushroom mixture to the skillet and cook, allowing the mushrooms to release their moisture, about 8-10 minutes — salt and pepper to taste. Transfer the mushroom mixture to a small bowl. Set aside to cool.
Once the fillet has cooled, lighty brush it all over with Dijon mustard. Set aside.
Cut a piece of plastic wrap about a foot and half long and place it on the countertop. Shingle the slices of prosciutto in the center of the plastic wrap, laying them out so they overlap. Spread a thin layer of the mushroom duxelles over the prosciutto slices.
Place the fillet on top of the mushroom-covered prosciutto. Tightly roll the fillet in the duxelles and proscuitto, forming a barrel. Secure the shape by twisting the ends of the plastic wrap. Chill in the refrigerator for 30 minutes.
Preheat the oven to 400 degrees.
Unfold the puff pastry onto a lightly floured surface. Use a rolling pin, gently roll the puff pastry sheet slightly larger in size, about 20 percent in both widths and lengths.
Remove the fillet from the refrigerator and gently unwrap from the plastic wrap. Place the fillet in the middle of the puff pastry dough. Fold over the sides to cover the fillet.
Prepare the egg wash. In a small bowl, whisk two yolks and milk until well combined. Using a pastry brush, brush the edges of the pastry dough with the egg wash to seal the dough. Trim any excess dough and save for decoration if desired. Brush trimmed ends with egg wash.
Transfer the beef wellington to a greased baking sheet or baking pan. Brush the entire surface of the beef wellington with the egg wash, then score the top of the pastry by making a few slits with a paring knife. Adorn your beef wellington with lattice or other decorative cut-outs. Dip your fingertips in water, and run them along your decorative elements to help them stick to the dough. Brush with egg wash.
Bake for 35 to 45 minutes or until the pastry is golden brown, and the beef wellington registers at 125 degrees on an instant-read thermometer. Allow the beef wellington to rest for 10 minutes before slicing. Cut into thick slices. Serve immediately. Enjoy!