Add the shallots, garlic, thyme, and cremini mushrooms to a food processor. Pulse 10–12 times until finely chopped, scraping the sides as needed. Transfer the mixture to a bowl.
2 medium shallots, 2 cloves garlic, 2 teaspoon thyme, 2 cups cremini mushrooms
Pat the beef tenderloin dry with paper towels. Coat all sides with Dijon mustard, then season with salt and black pepper.
1 tablespoon dijon mustard, 2 ¼ teaspoon salt, ½ teaspoon freshly ground black pepper
Heat vegetable oil in a large frying pan over medium-high heat. When shimmering, add the beef tenderloin and sear, turning occasionally, until browned on all sides (about 8 minutes). Remove the beef and refrigerate.
2 tablespoons vegetable oil, 2 ½ pound center-cut beef tenderloin roast
In the same pan, melt the butter over medium heat. Add the mushroom mixture and cook, stirring occasionally, until the mixture is dry and the mushrooms and pan begin to brown (about 15 minutes). Spread the mixture evenly onto a large plate and refrigerate for 30 minutes to an hour.
2 tablespoons unsalted butter
Lay a 2-foot-long sheet of plastic wrap horizontally on your work surface and dust it with flour.
All-purpose flour
Lay a large sheet of plastic wrap on your work surface and lightly dust it with flour. Arrange the prosciutto slices in overlapping rows, forming a rectangle large enough to fully wrap the beef. Spread the chilled mushroom mixture evenly over the prosciutto, leaving a 1/2-inch border at the edges.
5 ounces cold slices prosciutto
Place the beef tenderloin horizontally on the prosciutto at the edge closest to you. Use the plastic wrap to roll the prosciutto and mushroom layer tightly around the beef ensuring that the seam is face down. Twist the ends of the wrap to seal, and refrigerate for at least 30 minutes or up to 8 hours.
Preheat the oven to 350°F (180ºC) and line a baking sheet with parchment paper. Roll out the puff pastry on a lightly floured surface. Unwrap the beef and place it seam-side down on the pastry. Wrap the beef tightly in the pastry, trimming excess and sealing the edges with egg wash. Fold in the ends and brush them with egg wash as well.
1 puff pastry
Place the pastry-wrapped beef seam-side down on the baking sheet. Brush the entire surface with egg wash and sprinkle with flaky salt, if desired. Bake for 40–50 minutes, or until the internal temperature reaches 140–150°F (60–65ºC) for medium-rare. Cover loosely with foil if the pastry browns too quickly.
1 large egg, Flaky salt
Remove the Wellington from the oven and let it rest for 20 minutes on the baking sheet. Use a large, stiff spatula to transfer to a cutting board and slice crosswise into 1-inch pieces using a very sharp or serrated knife. Serve immediately.