Preheat the oven to 400 degrees F (200 degrees C).
Peel and cut the apples in small cubes.
Add brown sugar, and cinnamon, and cook, stirring, for a couple of minutes.
Unfold puff pastry sheets. Trim each sheet into a square.
Spoon apples in the centre of each square. Fold over from corner to corner into a triangle shape, and press edges together to seal with the help of a folk.
Bake until turnovers are puffed and lightly browned. Cool completely before glazing.
To make the glaze: Mix icing sugar and water together in a small bowl. Adjust the thickness by adding more sugar or water if necessary.
Drizzle glaze over the cooled turnovers.