Trim and season the beef: Pat the beef dry. Trim any surface silver skin if needed.
Season all over with 1–1.5 teaspoons kosher salt and plenty of black pepper. Let it sit at room temperature for 20–30 minutes.
Sear the beef: Heat a heavy skillet over medium-high. Add oil, then sear the beef on all sides until well browned, about 2–3 minutes per side.
Don’t overcook—this is just for color. Transfer to a plate to cool slightly. Brush all over with Dijon mustard while still warm.
Let cool to room temperature, then chill in the fridge 15–20 minutes.
Make the mushroom duxelles: In the same pan, melt butter over medium. Add mushrooms, shallots, garlic, and thyme with a pinch of salt. Cook, stirring, until the mixture is dry and deeply browned, 10–12 minutes.
If using wine, add it, then cook until fully evaporated. The duxelles should be paste-like with no visible moisture. Cool completely.
Prepare the prosciutto wrap: Lay a large piece of plastic wrap on your counter.
Overlap the prosciutto slices into a rectangle just wider than the beef and long enough to wrap around it. Spread the cooled duxelles evenly over the prosciutto.
Wrap the beef: Place the chilled, mustard-brushed beef at one edge of the prosciutto. Using the plastic wrap to help, roll the prosciutto and mushrooms tightly around the beef.
Twist the plastic wrap ends to secure a tight log. Chill 15–20 minutes to set the shape.
Wrap in puff pastry: Lightly flour your surface. Roll the puff pastry into a rectangle about 1/8 inch thick.
Unwrap the prosciutto-wrapped beef and place it on the pastry. Trim excess pastry so there’s about a 1-inch overlap seam. Brush edges with a little egg wash, then roll the pastry around the beef.
Seal the seam and fold the ends underneath. Place seam-side down. Brush all over with egg wash.
Optionally, score a light crosshatch pattern on top and sprinkle a little flaky salt.
Chill again: Transfer the wrapped Wellington to the fridge for 15–30 minutes. This helps the pastry stay crisp and hold its shape.
Preheat the air fryer: Preheat to 390°F (200°C) for 5 minutes. Lightly oil or spray the basket to prevent sticking.
Air fry: Place the Wellington in the basket seam-side down.
Air fry at 390°F for 10 minutes to set the color. Reduce to 360°F (182°C) and cook another 12–18 minutes, depending on thickness and desired doneness.
Check temperature: Use an instant-read thermometer inserted into the center. Target 120–125°F for rare, 130°F for medium-rare, or 135–140°F for medium.
Remember it will rise 5°F as it rests.
Rest and slice: Transfer to a board and rest 10–15 minutes. Slice with a sharp serrated knife into 1–1.5-inch slices. Serve immediately.