In a medium saucepan over medium heat, combine diced apples, brown sugar, cornstarch, cinnamon, and lemon juice.

Cook, stirring occasionally, until apples are soft and caramelized, about 10 minutes. Remove from heat and let cool.

Preheat oven to 400°F. Roll out the thawed puff pastry sheets and cut each into four squares.

Spoon the cooled apple mixture onto one half of each square, leaving a border. Mix the beaten egg with water to make an egg wash. Brush the edges of the pastry with the egg wash, fold over to form a triangle, and press edges to seal.

Place turnovers on a baking sheet lined with parchment paper. Cut small slits in the tops to vent steam. Brush with remaining egg wash. Bake for 20 minutes or until golden brown.

Mix powdered sugar and milk to create a glaze, adding more milk if needed until it reaches your desired consistency. Drizzle over warm turnovers. Serve warm or at room temperature.