In a medium saucepan over medium heat, melt the butter and add in the diced apples. Cook for about five minutes until softened.
Reduce heat to low, stir in brown sugar, granulated sugar, cornstarch, cinnamon, and salt. Simmer for 3-5 minutes until apples are tender.
Roll each sheet of puff pastry into an 11-inch square and cut into four equal squares.
Place 1-2 tablespoons of cooled apple filling in the center of each pastry square.
Whisk together egg and milk for egg wash. Brush on two sides of pastry square, fold to create a triangle, and crimp edges.
Cut slits in the top of each turnover for steam to escape and brush with egg wash.
Preheat oven to 375°F (190°C) and chill assembled turnovers in the refrigerator for 15 minutes.
Bake for 20-25 minutes until golden brown and puffed up.
Mix powdered sugar and milk for glaze and drizzle over warm turnovers.