Prepare and Sugar the Pastry: Place the defrosted puff pastry on top of the sugar and lightly roll it into an evenly thick square or rectangle, repairing any cracks from folding. If using a rectangle, position it with the long edge facing you. Lightly brush the pastry with some of the beaten egg, if using, then sprinkle sugar evenly over the surface. Flip the pastry so the sugared side is facing down, brush the exposed side lightly with egg wash, and sprinkle the remaining sugar evenly over it. Finely Grind the Chocolate: Place the bittersweet chocolate in a mini chopper and blitz until it becomes a fine dust. Sprinkle the ground chocolate evenly over the sugared surface of the pastry.
Fold the Pastry into a Log: Fold the long edge nearest you toward the center, bringing it about one-quarter of the way across the pastry. Fold it again until it reaches the center. Repeat the same folding process with the opposite long edge. Finally, fold one side over the other to form a compact log of puff pastry. Slice and Arrange: Line the air fryer basket with parchment paper. Cut the pastry log into ½-inch slices, then lay each slice flat on the parchment, leaving a little space between the pieces.
Air-Fry the Palmiers: Air-fry the palmiers at 400°F for 10 minutes, turning them over halfway through the cooking time. Continue cooking until they are crisp and golden.