For the dipping sauce, mix all the ingredients in a bowl with a large spoon or whisk.
Taste and adjust with salt and pepper as necessary.
Spread the first puff pastry crust dough on a large chopping board.
Spread out the cheese all over the puff pastry, and shred some of the ham on top.
Fold the two ends of the pastry, rolling towards the middle. Line the two rolls so that they sit top of each other.
Cut the puff into rolls for equal bite-size pieces.
Move each roll to the air fryer tray, leaving enough room for them to expand.
Preheat the air fryer to 400°F (200°C).
Crack open the egg into a bowl and mix it with a spoon to make an egg wash.
Apply the egg wash to the top of the cheese rolls with a silicone baking brush (or teaspoon).
Place the air fryer tray with the rolls in the air fryer and cook for 15 minutes until golden brown. (If possible, turn the rolls at the halfway point so that they cook evenly.)
Take out of the air fryer and let cool for 5 minutes or so.
Transfer the sauce to a individual dipping sauce bowls, and serve alongside the cheese rolls.