1. Pat the beef tenderloin dry with paper towels, then season it all over with kosher salt and freshly ground black pepper.

2. Heat the olive oil in a large heavy skillet over medium-high heat until shimmering, then sear the beef on all sides, including the ends, until well browned, about 2 to 3 minutes per side.

3. Transfer the seared beef to a plate and let it cool for 10 minutes, then brush it all over with Dijon mustard while it is still slightly warm.

4. In the same skillet, reduce the heat to medium and add the butter. Once melted, stir in the finely chopped mushrooms and a pinch of salt and cook, stirring often, until the mushrooms release their moisture and it fully evaporates.

5. Add the minced shallot and garlic to the mushrooms and cook until softened and fragrant, then stir in the chopped thyme leaves.

6. Pour in the white wine or sherry to deglaze the pan, scraping up any browned bits, and cook until the liquid has completely reduced and the mushroom mixture is thick and almost paste-like.

7. Spread the mushroom duxelles onto a plate or small baking sheet and let it cool completely to room temperature.

8. Lay a large sheet of plastic wrap on your work surface and arrange the prosciutto slices in slightly overlapping rows to form a rectangle large enough to wrap around the beef.

9. Spread the cooled mushroom duxelles evenly over the prosciutto, leaving a small border around the edges.

10. Place the Dijon-brushed beef tenderloin along one long edge of the prosciutto rectangle and, using the plastic wrap to help you, roll it up tightly so the prosciutto and mushrooms fully encase the beef.

11. Twist the ends of the plastic wrap to secure the log and refrigerate for at least 30 minutes so it firms up.

12. While the beef chills, lightly flour your work surface and roll the puff pastry into a rectangle large enough to wrap the beef log, about 1/8 inch thick.

13. Trim the edges of the pastry to make neat sides, reserving any scraps for decorative cutouts if desired.

14. In a small bowl, whisk together the egg and the water or cream to make an egg wash.

15. Remove the wrapped beef log from the refrigerator, unwrap it from the plastic, and place it near one long edge of the puff pastry.

16. Brush the exposed edges of the pastry lightly with egg wash, then roll the pastry tightly around the beef, trimming any excess dough and folding the ends underneath so the beef is completely enclosed.

17. Transfer the wrapped Wellington to a parchment-lined baking sheet, seam side down, and brush the entire surface with more egg wash.

18. If you like, use the tip of a sharp knife to lightly score a crisscross pattern on the pastry without cutting all the way through, and add any decorative pastry cutouts to the top.

19. Refrigerate the assembled Wellington for 20 to 30 minutes while you preheat the oven to 400°F (200°C).

20. Bake the Wellington for 30 to 40 minutes, or until the pastry is deep golden brown and an instant-read thermometer inserted into the center of the beef registers 120 to 125°F (49 to 52°C) for medium-rare.

21. If the pastry is browning too quickly, loosely tent the Wellington with foil for the last several minutes of baking.

22. Transfer the baked Wellington to a cutting board and let it rest for 10 to 15 minutes so the juices redistribute.

23. Slice the Juicy Beef Wellington into thick rounds with a sharp serrated knife and serve immediately with your favorite sides and sauce.