Preheat the oven to 400 degrees F. Remove the puff pastry from the freezer and thaw.
Melt butter over medium heat in a medium pot. Add diced apples and cook, stirring occasionally until softened (5 minutes).
Reduce heat to low and stir in the brown sugar, cinnamon, and salt. Simmer until the apples are soft and caramelized, and then remove from heat and cool.
Sprinkle the flour to prevent the dough from sticking and, using a rolling pin, roll the first sheet of thawed pastry to 11 inches square. Use a pizza cutter to cut into 4 equal squares.
Place cooled apple mixture in the center of each square, leaving at least a 1/2-inch border.
Beat egg and water. Brush egg wash over edges of the pastry. Bring the edges together and crimp tightly along the edges with a fork to seal and cut 3 slits into top to allow pastries to vent.
Transfer to a parchment-lined baking sheet, keeping the pastries at least 1 inch apart.
Place in the fridge for 20 minutes.
Remove the pastries from the fridge and brush the tops with the remaining egg wash and bake for 20 minutes or until golden brown and puffed.
Combine the powdered sugar and 1 tablespoon heavy whipping cream and stir. If the glaze is too thick, add more heavy whipping cream until you get the desired consistency and drizzle glaze over the turnovers.