Preheat the oven to 400°F. Line two baking sheets with parchment paper.

In a large skillet over medium heat, melt the butter. Add the apples and cook for a few minutes while stirring frequently. Add the brown sugar, cinnamon, and salt, and stir to coat the apple pieces. Cook for 5 to 10 minutes or until the apples are softened and become syrupy. Reduce the heat to low.

Sprinkle in the cornstarch and stir until the juices boil and thicken, about 1 minute. Transfer to a bowl. Let cool for 15 minutes then refrigerate until chilled, about 30 minutes.

When the apples are chilled, roll each thawed puff pastry sheet out on a lightly floured surface into a 12-inch square. Cut each sheet into 4 equal squares.

Place a square of puff pastry on the baking sheet and brush the edges of each square with the egg wash. Place a few tablespoons of filling in each square. (You may have a little bit of filling left over depending on how small you diced the apples and how much they cooked down.) Fold one point of the puff pastry over the filling to the opposite point, creating a triangle. Crimp and seal in the filling by pressing the lines of a fork along both straight edges. Brush the top with more egg wash and cut a few small slits in the top. Sprinkle with sugar, if desired.

Bake for 18 to 20 minutes or until the pastry is golden and puffed. Let cool for at least 15 minutes.

In a small mixing bowl, combine the powdered sugar and water and whisk until smooth. You can add a bit more water if the consistency needs to be thinned out. Drizzle over the warm turnovers and enjoy!