Season the beef tenderloin steaks generously with salt and pepper. Sear the steaks in olive oil in a hot skillet for 1-2 minutes per side until browned. Remove from heat and brush lightly with Dijon mustard. Let cool slightly.
Prepare the duxelles: Cook the chopped mushrooms, minced shallot, and thyme in the same skillet over medium heat until all moisture has evaporated, about 8-10 minutes. Stir in the sherry and cook until evaporated. Season with salt and pepper. Spread the duxelles mixture onto a plate to cool completely.
Lay two slices of prosciutto flat on a piece of plastic wrap, slightly overlapping. Spread half of the cooled duxelles evenly over the prosciutto. Place one seared steak on top.
Wrap the prosciutto and duxelles tightly around the steak using the plastic wrap, twisting the ends to form a neat cylinder. Chill both wrapped steaks for at least 20 minutes to firm up.
Lightly dust a clean surface with flour. Roll the puff pastry sheet into a rectangle large enough to wrap both steaks completely, aiming for about 1/8 inch thickness. Cut the pastry in half to create two equal rectangles.
Remove the plastic wrap from one chilled steak. Place the steak near one edge of a pastry half. Brush the edges of the pastry with the beaten egg wash. Fold the pastry over the steak, pressing firmly to seal the edges. Trim excess pastry. Place the sealed Wellington seam-side down on a parchment-lined baking sheet. Repeat with the second steak.
Brush the tops and sides of both Wellingtons evenly with the remaining egg wash. Score the top lightly with the back of a knife in a decorative pattern, taking care not to cut through the pastry. Chill for another 15 minutes.
Preheat your oven to 400 degrees Fahrenheit (200 degrees Celsius).
Bake for 20-25 minutes, or until the pastry is golden brown and puffed. Use a meat thermometer inserted into the center of the steak to check the internal temperature for medium-rare (130-135 degrees Fahrenheit).
Remove from the oven and let the individual Wellingtons rest on the baking sheet for 5-10 minutes before slicing or serving.
Notes
Chilling the duxelles and the wrapped steaks helps prevent the pastry from becoming soggy during baking.
For the best pastry rise, make sure your oven is fully preheated before placing the Wellingtons inside.
If the pastry browns too quickly before the center reaches temperature, loosely tent the Wellingtons with aluminum foil for the remainder of the cooking time.