Spread the first puff pastry crust dough on a large chopping board.
Spread out the puff pastry and spoon on the boursin cheese, 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 puff pastry roll to a lined baking 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 puff pastry sausage rolls with a silicone baking brush (or teaspoon).
Place the baking tray with the puff pastry boursin rolls in the oven and cook for 8-12 minutes until golden brown. (If possible, turn the rolls at the halfway point so that they cook evenly.)
Take out of the oven and let cool for 5 minutes or so. Serve while warm.