Finely chop the pistachios in a blender until coarsely ground.
In a large bowl, beat the butter with sugar using a hand mixer until well combined.
Add the pistachios, cardamom, ginger, and salt to the bowl, mixing thoroughly with the hand mixer until smooth.
Line a countertop with parchment paper and lightly dust it with flour.
Roll out the puff pastry on the parchment paper.
Spread the pistachio mixture evenly over the puff pastry, leaving a 4 cm border on one end.
Roll the pastry into a cylinder and cut it into 8 equal pieces.
Score three diagonal lines on the top of each roll.
In a small bowl, whisk the egg yolk, then brush the top of each roll with the yolk using a pastry brush.
Place the rolls into the air fryer basket and cook at 160°C (320°F) for 28-30 minutes. During the last 10 minutes, flip the rolls to ensure even cooking on both sides.