Preheat the oven to 400 degrees F. Line a sheet pan with parchment paper, set aside.
In a smaller pan over medium-low heat, melt the butter. Then add the brown sugar and cinnamon to the pan. Stir until the sugar starts to dissolve.
Add the grated apple and stir to combine. Place a lid over the top and cook until soft, stirring occasionally, this will take about 10 minutes.
In a small bowl, add the apple juice and cornstarch and stir together until combined until you create a slurry.
Slowly pour the slurry mixture into the apple mixture, and cook for 1 additional minute, stirring constantly. The mixture will be thick, remove from the heat and set aside.
On a lightly floured clean work surface, place one sheet of puff pastry.
Roll it out into a 12x9-inch rectangle.
Then cut into thirds along the seam of the pastry.
Cut the thirds in half, so you have 6 rectangles.
Place the rectangles onto the prepared sheet pan making sure not to touch.
Cut the second puff pastry sheet the same way, place these to the side and cover with a clean kitchen towel making sure they don’t dry out.
To assemble, evenly distribute the apple filling into the center of each pastry. Spread it out leaving ½ inch border around the edges.
In a small bowl, beat the egg with a splash of water and brush the egg wash along the exposed edges of the pastry.
Take one of the remaining pastry rectangles and place it on top of the filling.
Press down firmly along the edges to make sure the two pastries stick together. Repeat with all the rectangles.
Brush the tops lightly with the egg wash.
Place in the oven and bake for 13-15 minutes until golden brown.
Remove from the oven and let them cool on the pan for 10 minutes, then transfer to a wire rack to cool completely.
In a small bowl, stir together the powdered sugar, milk, and vanilla extract. Start with 1 tablespoon of milk at first. If it seems too thick, add up to 1 tablespoon more milk, adding just a little bit at a time. You want the icing to be very thick yet pipeable.
Once the pastries are cooled, place the glaze into a piping bag or plastic baggie and snip off a very small piece of a corner.
Pipe zig-zag lines of icing on top.
Enjoy them immediately or let them sit for about 15-30 minutes until the icing hardens.