Preheat your oven to 400°F. Line two baking sheets with parchment paper and set aside.
Add the diced apples, butter, brown sugar, cinnamon, and salt to a small saucepan. Cook over medium-low heat, stirring occasionally, until the apples soften and release their juices (about 5-10 minutes). Remove from heat and let the mixture cool slightly.
Unfold the puff pastry sheets on a lightly floured surface. Using a sharp knife or pizza cutter, cut each sheet into 4 equal squares (cut once lengthwise, then once widthwise). Repeat with the second sheet so you have 8 squares total.
Place a spoonful of the apple filling in the center of each pastry square, making sure to drain off any extra liquid so the pastry doesn’t get soggy.
In a small bowl, whisk together the egg and water. Lightly brush the edges of each pastry square with the egg wash.
Fold each square over the filling to form a triangle. Press the edges together, then crimp with the tines of a fork to seal completely. Use a sharp knife to cut 2-3 small slits on the top of each turnover for ventilation. Brush the tops with the remaining egg wash.
Transfer the turnovers to the prepared baking sheets and bake for 20-22 minutes, or until golden brown and puffed. Allow them to cool on the baking sheet for a few minutes.
While the turnovers cool, make the glaze: whisk the powdered sugar and heavy cream in a small bowl until smooth.
Drizzle the glaze over the turnovers.
Serve warm or at room temperature.