11. Preheat the air fryer to 180°C (350°F). Place sweet potato, beetroot, half onion, garlic, and rosemary in the air fryer basket, drizzle with a little oil. Cook for 10 minutes, then transfer to a food processor with mixed nuts. Process until a thick paste forms. Shape the paste into a log on plastic wrap, roll tightly, and refrigerate.
22. For duxelles: heat olive oil in a pan and sauté finely chopped onion and mushrooms over medium heat for 10-15 minutes until liquid evaporates. Season with salt and pepper, then let cool completely.
33. Roll out puff pastry on a floured surface. Spread cooled duxelles evenly over pastry. Place the beet-nut log at one end and roll the pastry tightly around it. Wrap in plastic wrap and refrigerate for at least 30 minutes.
44. Remove the roll from the fridge, brush all over with beaten egg, and place in one air fryer basket. In the second basket (if dual-zone) or a separate tray, toss potato chunks, carrot rounds, parsnip slices, and Brussels sprouts with oil and salt. Use SYNC function to cook both simultaneously: set Wellington basket to 20 minutes at 180°C (350°F), and vegetables to 10-15 minutes (they may be done earlier; adjust as needed).
55. While cooking, prepare vegetarian gravy according to package instructions. Once done, let the Wellington rest for a minute, then slice thickly and serve with roasted vegetables and gravy.