Pat the 1 lb beef tenderloin center-cut trimmed of silver skin completely dry with paper towels and season all over with ½ tsp kosher salt and ¼ tsp black pepper freshly ground. Heat 1 tbsp olive oil in a cast iron skillet over high heat until it just begins to smoke. Sear the 1 lb beef tenderloin center-cut trimmed of silver skin on all sides — including the ends — for about 1 minute per side, until deeply browned all over. This should take about 4–5 minutes total. Transfer to a plate and let cool for 10 minutes.

Once the 1 lb beef tenderloin center-cut trimmed of silver skin has cooled slightly, brush it all over with a thin, even layer of Dijon mustard. Place in the refrigerator uncovered for at least 20 minutes (or up to 1 hour) to chill and set the 1 tbsp Dijon mustard.

Pulse the 10 oz cremini mushrooms finely chopped or pulsed in a food processor in a food processor until very finely chopped (or chop by hand). Melt 1 tbsp unsalted butter in the same cast iron skillet over medium-high heat. Add the 1 small shallot finely minced and cook for 1 minute, then add the 2 cloves garlic minced and cook 30 seconds more. Add the 10 oz cremini mushrooms finely chopped or pulsed in a food processor and 1 tsp fresh thyme leaves, season with ½ tsp kosher salt, and cook, stirring frequently, for 10–12 minutes until all the moisture has evaporated and the mixture is dark, dry, and paste-like. Spread onto a plate and refrigerate until completely cool, about 15 minutes.

Lay a large sheet of plastic wrap on your work surface. Arrange the 6 slices prosciutto thin slices slices in a single, overlapping layer to form a rectangle roughly 10x8 inches — wide enough to wrap the 1 lb beef tenderloin center-cut trimmed of silver skin and long enough to cover it end to end. Spread the cooled duxelles evenly over the 6 slices prosciutto thin slices in a thin, uniform layer, leaving a 1-inch border on the long edges.

Place the chilled 1 lb beef tenderloin center-cut trimmed of silver skin along the bottom edge of the slices prosciutto thin slices. Using the plastic wrap to help, tightly roll the 6 slices prosciutto thin slices and duxelles around the 1 lb beef tenderloin center-cut trimmed of silver skin, twisting the ends of the plastic wrap like a candy wrapper to form a tight, compact log. Refrigerate for at least 20 minutes (or up to 4 hours).

Preheat your oven to 425°F. Line a baking sheet with parchment paper. On a lightly floured surface, unfold one sheet of thawed 1 package frozen puff pastry and roll it out slightly to about 12x10 inches. Brush the entire surface with 1 egg beaten with 1 tbsp water wash.

Unwrap the chilled 1 lb beef tenderloin center-cut trimmed of silver skin log and place it in the center of the frozen puff pastry. Roll the 1 package frozen puff pastry tightly around the 1 lb beef tenderloin center-cut trimmed of silver skin, pressing to seal the seam firmly. Tuck the ends under like a gift wrap and press to seal. Place seam-side down on the prepared baking sheet. Brush the entire surface generously with 1 egg beaten with 1 tbsp water wash. Use a sharp knife to lightly score a crosshatch or diagonal pattern on top (do not cut through). Sprinkle with ¼ tsp flaky sea salt for finishing if using. Refrigerate for 10 minutes before baking.

Bake at 425°F for 22–28 minutes, until the 1 package frozen puff pastry is deep golden brown and an instant-read thermometer inserted into the center of the beef tenderloin center-cut trimmed of silver skin reads 125°F for medium-rare (the temperature will rise 5°F as it rests). For medium, pull at 130–132°F. Do not open the oven door during the first 20 minutes.

Transfer the Wellington to a cutting board and let it rest, uncovered, for 8–10 minutes. Use a sharp bread knife to slice into two thick portions and serve immediately.