Pat the beef tenderloin completely dry with paper towels. Season generously on all sides with kosher salt and black pepper.

Heat olive oil in a large heavy skillet (cast iron or stainless) over high heat until smoking. Sear the beef on all sides, including the ends, for about 1 to 2 minutes per side until a deep mahogany crust forms. Total searing time should be 6 to 8 minutes.

Transfer the seared beef to a plate. Immediately brush all over with Dijon mustard using a pastry brush. Allow to cool completely to room temperature, then refrigerate uncovered for at least 30 minutes.

In the same skillet over medium-high heat, melt butter. Add shallots and garlic and cook for 2 minutes until softened.

Add the finely chopped mushrooms, thyme, salt, pepper, and sherry if using. Cook, stirring frequently, for 12 to 15 minutes until all the liquid has evaporated and the mixture is nearly dry and dark. The mushrooms should look like a thick, almost paste-like consistency.

Spread the duxelles onto a plate or baking sheet and refrigerate until fully cooled, about 20 minutes.

Lay a large sheet of plastic wrap on your work surface. Arrange the prosciutto slices in a rectangle slightly wider and longer than your beef tenderloin, overlapping them by about half an inch.

Spread the cooled mushroom duxelles evenly over the prosciutto in a thin, even layer.

Place the chilled, mustard-coated beef at the near edge of the prosciutto. Using the plastic wrap, tightly roll the prosciutto and duxelles around the beef, twisting the ends of the plastic wrap tightly to form a firm, uniform log. Refrigerate for at least 30 minutes or up to 24 hours.

Lightly flour your work surface and roll the puff pastry out to a rectangle large enough to encase the beef roll completely. Unwrap the chilled beef roll and place it at the near edge of the pastry. Brush the far edges of the pastry with egg wash.

Roll the beef tightly in the pastry, pressing the seam firmly to seal. Tuck the ends under and press to seal. Place seam-side down on a parchment-lined baking sheet.

Brush the entire surface generously with egg wash. Score a light decorative pattern on top with the back of a knife, being careful not to cut all the way through. Sprinkle with flaky sea salt. Refrigerate for 15 to 20 minutes while the oven preheats.

Preheat the oven to 425°F (220°C).

Bake the Wellington for 25 to 30 minutes until the pastry is deeply golden brown and an instant-read thermometer inserted into the center of the beef reads 125°F to 130°F for medium-rare.

Transfer to a cutting board and rest uncovered for 10 full minutes before slicing with a sharp serrated knife into 1.5-inch rounds. Serve immediately.