01 - Preheat your oven to 400°F (200°C). Line a standard baking sheet with parchment paper to prevent sticking.
02 - Gently pat the beef fillets dry with paper towels. Season generously with salt and freshly ground black pepper. Heat 1 tablespoon of olive oil in a skillet over high heat. Sear the fillets for 1 to 2 minutes on all sides until a rich brown crust forms. Remove from the pan and immediately brush all surfaces with Dijon mustard. Allow the seared beef to cool completely.
03 - In the same skillet, melt 2 tablespoons of unsalted butter over medium heat. Add the finely chopped shallot and minced garlic, sautéing until softened, about 2 minutes. Incorporate the finely chopped mushrooms and fresh thyme leaves. Cook, stirring occasionally, until all moisture has evaporated and the mixture achieves a paste-like consistency, typically 8 to 10 minutes. Season with salt and pepper to taste, then set aside to cool.
04 - Lay out a large piece of cling film or plastic wrap on a clean work surface. Arrange the prosciutto slices, overlapping slightly, to form a rectangle. Evenly spread half of the cooled mushroom duxelles over the prosciutto.
05 - Place one seared beef fillet on top of the duxelles-covered prosciutto. Cover the beef with the remaining duxelles. Carefully use the cling film to tightly roll the prosciutto around the beef and duxelles, forming a compact log. Press firmly to ensure a tight seal. Repeat this process for the second fillet. Chill both wrapped fillets in the refrigerator for 15 minutes to firm up.
06 - On a lightly floured surface, roll out the puff pastry to a thickness of about 1/8 inch (3 mm), ensuring it is large enough to encase both beef logs with a slight overlap. Divide the pastry into two equal pieces.
07 - Remove the beef logs from the cling film. Place each fillet in the center of a pastry piece. Brush the edges of the pastry with the beaten egg wash. Carefully fold the pastry over the beef, sealing the edges tightly underneath the fillet. Place each Wellington seam-side down on the prepared baking sheet. Brush the tops of both Wellingtons with additional egg wash. Optionally, decorate with pastry trimmings.
08 - Bake in the preheated oven for 20 to 25 minutes, or until the puff pastry is golden brown and crisp, and a meat thermometer inserted into the center of the beef registers an internal temperature of 122–131°F (50–55°C) for medium-rare. Allow the Beef Wellingtons to rest for 10 minutes before carefully slicing and serving.