Unfold the thawed puff pastry on a lightly floured surface and roll it out just enough to smooth the seams. Place the brie wheel in the center of the pastry.
Drizzle the top of the brie with honey, then scatter the chopped walnuts and fresh thyme leaves over it. Press the toppings gently so they stay in place.
Fold the puff pastry up and over the brie, pulling opposite corners toward the center. Pinch and press the seams together tightly to seal the brie completely inside. Trim away any excess pastry if it becomes too thick in one spot.Flip the wrapped brie seam-side down and brush the entire surface with beaten egg.
Preheat the air fryer to 340 degrees F for 3 minutes. Line the basket with a small piece of parchment paper, then place the wrapped brie on top seam-side down.
Air fry at 340 degrees F for 14 to 16 minutes, until the puff pastry is deep golden brown and puffed. Check halfway through and if the top is browning too quickly, loosely tent a small piece of foil over it.
Carefully transfer the baked brie to a serving board and let it rest for 5 minutes so the cheese sets just slightly. Sprinkle with a pinch of flaky sea salt, slice into the top to reveal the melty cheese, and serve with crackers and sliced baguette.