Prep the beef: Pat the beef dry. Season all sides generously with salt and pepper.
Let sit at room temperature for 15 minutes while you prep the mushrooms.
Make the mushroom duxelles: Heat olive oil and butter in a skillet over medium heat. Add mushrooms, shallot, and a pinch of salt. Cook, stirring, until the mixture releases its moisture and becomes dry and concentrated, 8–10 minutes.
Add garlic and thyme; cook 1 minute more. Remove from heat and cool completely.
Sear the beef: Heat the same skillet over medium-high. Sear the beef for 45–60 seconds per side to brown, not cook through.
Transfer to a plate and brush all over with Dijon. Let cool. Cold components help keep the pastry crisp.
Prep pastry and prosciutto: Lightly flour your surface. Roll the puff pastry to smooth creases, then cut into 4 rectangles large enough to wrap each piece of beef.
If using prosciutto, lay a slice on each rectangle.
Assemble: Spread a tablespoon of mushroom duxelles over the prosciutto or directly on the pastry. Place a beef medallion in the center. Fold the pastry up and over the beef, sealing seams firmly.
Trim excess pastry if needed. Place seam-side down. Brush with egg wash.
Score lightly on top for vents.
Chill: Refrigerate the wrapped Wellingtons for 15–20 minutes. Chilling helps prevent blowouts and keeps the pastry flaky.
Preheat the air fryer: Set to 390°F (200°C) for 3–5 minutes. Lightly spray the basket or use a parchment liner with perforations.
Air fry: Arrange Wellingtons in a single layer with space between. Air fry at 390°F (200°C) for 10–14 minutes for medium-rare, depending on thickness and your air fryer model. Internal temp for medium-rare: 125–130°F (52–54°C) after resting.
Rest and serve: Let rest 5 minutes.
The carryover cooking will bring them to a perfect pink center. Serve hot with a simple pan sauce, peppercorn sauce, or a side of greens.