01 - Preheat your oven to 400°F. Line a baking sheet with parchment paper, preparing it for the Wellingtons.
02 - Thoroughly pat the beef fillets dry with paper towels and season generously with kosher salt and freshly ground black pepper. Heat 1 tablespoon of olive oil in a large skillet over high heat. Sear the fillets on all sides for 1–2 minutes, just until they achieve a deep brown crust. Remove the seared beef from the pan and immediately brush all sides with Dijon mustard. Set aside to cool completely.
03 - In the same skillet (or a clean one), melt 2 tablespoons of unsalted butter over medium heat. Add the finely minced shallot and garlic, cooking until softened, which should take about 2 minutes. Incorporate the finely chopped mushrooms and fresh thyme leaves. Continue to cook, stirring frequently, until all the moisture has evaporated and the mixture forms a thick, paste-like consistency, approximately 8–10 minutes. Season the duxelles with kosher salt and freshly ground black pepper. Allow the mixture to cool completely.
04 - Lay out a large piece of plastic wrap on a clean work surface. Arrange the 4 slices of prosciutto, overlapping them slightly to form a rectangular base. Evenly spread half of the cooled mushroom duxelles over the prosciutto layer.
05 - Place one cooled, mustard-brushed beef fillet in the center of the duxelles-covered prosciutto. Cover the beef with the remaining half of the duxelles. Using the plastic wrap, carefully and tightly roll the prosciutto around the beef and duxelles, creating a compact log. Press firmly to ensure a tight seal. Repeat this process for the second fillet. Chill both assembled beef logs in the refrigerator for at least 15 minutes to firm up.
06 - On a lightly floured surface, roll out the puff pastry to a rectangle large enough to enclose both beef logs with a slight overlap. Cut the pastry into two equal pieces.
07 - Remove the chilled beef logs from the plastic wrap. Place one beef log in the center of a puff pastry piece. Brush the edges of the pastry with the lightly beaten egg wash. Carefully fold the pastry over the beef, sealing the edges tightly and ensuring the seam is underneath the Wellington. Trim any excess pastry. Transfer the wrapped Wellington, seam-side down, to the prepared baking sheet. Repeat for the second Wellington. Brush the tops of both Wellingtons with additional egg wash. (Optional: Decorate with pastry trimmings for an elegant finish.)
08 - Bake the Wellingtons for 20–25 minutes, or until the pastry is puffed, golden brown, and crisp. For medium-rare beef, the internal temperature should register between 122–131°F on a meat thermometer. Once baked, remove the Wellingtons from the oven and allow them to rest for 10 minutes before carefully slicing and serving.