In a medium saucepan over medium heat, melt the butter and add in the diced apples. Cook for about 5 minutes until they start to soften but still hold their shape.
Lower the heat and stir in brown sugar, granulated sugar, cornstarch, cinnamon, and salt. Cook for an additional 3-5 minutes until the apples are soft but not mushy; remove them from heat and let cool completely.
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 using a pizza cutter.
Spoon 1-2 tablespoons of apple filling into the center of one square while being careful not to touch the edges; this ensures proper sealing later.
In a small bowl, beat together one egg with one tablespoon of milk for an egg wash. Brush this mixture onto two sides of each pastry square before folding one corner over to meet another corner, forming a triangle; press down on edges to seal.
Preheat your oven to 375°F while chilling assembled pastries in the refrigerator for about 15 minutes before baking them on lined baking sheets until golden brown for approximately 20-25 minutes.