In a small bowl, lightly beat the egg with the water and set aside.
Unroll the thawed puff pastry sheet(s) and cut into 8 rectangles. My 1 pound sheet was approximately 15x13 inches and I cut it into 8, but some sheets are only half this size.
Place approximately 2 tablespoons of filling onto one end of each rectangle.
Brush the egg wash on the 3 edges of the pastry around the filling.
Fold the other end of the rectangle over the filling and press all 3 edges with a fork to seal. Poke a few holes in the top of each turnover with the fork.
Brush tops of turnovers with the egg wash.
Spray the air fryer basket with non-stick spray or line with a piece of parchment paper and place the turnovers in the basket.
Set the air fryer to 320 degrees for 17 minutes. Place any turnovers that did not fit in the basket on a parchment lined baking sheet and set in the refrigerator until ready to bake.
Remove the baked turnovers from the fryer and move them to a cooling rack. Proceed to bake second batch if you couldn't fit them all in your fryer.
Once the turnovers are cool, drizzle with icing and serve.