In a medium saucepan, over medium heat, add butter to melt. Stir in diced apples and cook until softened, about 5 minutes.
Reduce heat to low and stir in brown sugar, cinnamon, nutmeg, lemon juice, flour and salt. Continue to simmer 3 minutes until apples are soft and caramelized. Remove from heat and set aside to cool.
On a lightly floured surface, use a lightly floured rolling pin to roll the first sheet of thawed puff pastry to an 11" square. With a pizza cutter or sharp knife, cut into 4 equal-sized squares. Place a ¼ cup cooled apple mixture in center of each square, leaving at least a 1/2" border. Filling is juicy so make sure to not get too much liquid when scooping mixture.
Place a ¼ cup of the cooled apple mixture into the center of each square, leaving at least a 1/2" border.
Thoroughly beat together 1 egg and 1 Tbsp water. Lightly brush egg wash lightly on edges of the pastry (just enough to seal), bring the edges together and crimp tightly along the edges with a fork to seal. Save the rest of the egg wash for brushing on right before baking.
Transfer to a parchment-lined baking sheet, spaced about 1" apart. With a sharp knife, cut 2-3 small slits in the top of each turnover. Refrigerate for 20 minutes (this helps the filling from leaking out.)
Position a rack in the center of your oven and preheat oven to 400oF (205oC). Brush the tops of each turnover with egg wash and bake 20-23 minutes or until golden brown and puffed.
While turnovers are still warm, stir together powdered sugar, vanilla, and milk. Adjust consistency if needed. Drizzle glaze over turnovers.