Pat the beef tenderloin dry with paper towels to remove excess moisture, then season it evenly on all sides with the salt and black pepper.

Heat the olive oil in a skillet over medium-high heat until hot, then sear the beef tenderloin on all sides, including the ends, for about 1 to 2 minutes per side until nicely browned. Transfer the seared beef to a plate to cool slightly.

In the same skillet, reduce the heat to medium and add the unsalted butter. Once melted, add the finely chopped cremini mushrooms, minced shallot, and minced garlic.

Cook the mushroom mixture, stirring often, until most of the moisture has evaporated and the mixture looks dry and fragrant, about 8 to 10 minutes. Stir in the chopped fresh thyme leaves, salt for the mushroom mixture, and black pepper for the mushroom mixture, then cook for 1 more minute. Remove from heat and let the mushroom mixture cool completely.

Brush the cooled beef tenderloin all over with the Dijon mustard, coating it in a thin, even layer.

Lay a sheet of plastic wrap on your work surface. Arrange the prosciutto slices slightly overlapping in a rectangle large enough to wrap around the beef tenderloin.

Spread the cooled mushroom mixture evenly over the prosciutto layer, pressing it gently so it adheres.

Place the mustard-coated beef tenderloin along one long edge of the prosciutto and mushroom layer. Using the plastic wrap to help, roll the prosciutto and mushroom layer tightly around the beef to create a neat log. Twist the ends of the plastic wrap to secure and refrigerate for 15 to 20 minutes to firm up.

While the wrapped beef chills, lightly dust your work surface with the all-purpose flour and roll out the puff pastry sheet into a rectangle large enough to fully enclose the beef log.

Remove the chilled beef log from the refrigerator and unwrap it from the plastic. Place it in the center of the puff pastry.

Fold the puff pastry over the beef, tucking in the sides and sealing the edges by pressing them together firmly. Trim any excess pastry if necessary and place the seam side down.

In a small bowl, beat the egg with the water to make an egg wash. Brush the entire surface of the wrapped pastry with the egg wash for a glossy, golden finish.

Use a sharp knife to lightly score the top of the pastry with shallow diagonal lines or a simple crisscross pattern, being careful not to cut all the way through.

Lightly brush the air fryer basket or tray with the olive oil for the air fryer basket to help prevent sticking.

Place the wrapped Beef Wellington into the air fryer basket seam side down, leaving a little space around it for air circulation.

Set the air fryer to 375°F (190°C) and cook the Beef Wellington for about 25 to 30 minutes, or until the pastry is deep golden brown and crisp. If you like, check the internal temperature of the beef with a meat thermometer; aim for about 125°F (52°C) for medium-rare.

Carefully remove the Beef Wellington from the air fryer and transfer it to a cutting board. Let it rest for 10 minutes to allow the juices to redistribute.

After resting, slice the Beef Wellington into thick slices with a sharp knife and serve immediately while the pastry is still crisp and the beef is warm and tender.