In a medium saucepan over medium heat, melt the butter and add in diced apples. Cook for about 5 minutes until they start to soften, then reduce heat to low. Add brown sugar, granulated sugar, cornstarch, cinnamon, and salt, cooking for an additional 3-5 minutes until the apples are tender but not mushy.
On a lightly floured surface, roll each sheet of puff pastry into an 11-inch square using a rolling pin. Cut each sheet into four equal squares.
Place 1-2 tablespoons of apple filling in the center of each square, being careful not to get any filling on the edges that need sealing.
In a small bowl, beat together one egg with one tablespoon of milk to create an egg wash. Brush this mixture on two adjacent sides of each square before folding one corner over to meet its opposite corner and form a triangle.
Press down on all edges firmly to seal them together and crimp with a fork for added security. Cut small slits in the tops of each turnover for steam release and brush them generously with more egg wash.
Preheat your oven to 375°F and refrigerate assembled turnovers for about 15 minutes before baking them on lined baking sheets spaced evenly apart. Bake for approximately 20-25 minutes until they turn golden brown and are puffed up beautifully.