Preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper and set it aside.
Peel and core the apples. Cut each apple into quarters, divide each quarter into three sections, and then chop the pieces finely.
Melt the butter in a medium saucepan over medium heat.
Add the prepared apples, brown sugar, cinnamon, salt, and vanilla extract. Stir until the apples are evenly coated.
Allow the mixture to simmer for approximately 5 minutes, stirring occasionally, until the fruit begins to soften. Remove the saucepan from the heat and leave the filling to cool while preparing the pastry.
Unroll both refrigerated pie crusts onto a clean, flat work surface. Using a round cutter or the rim of a glass, cut three circles from each crust.
Gather and reroll the remaining pastry scraps when necessary to obtain a total of six dough circles.
Place approximately ¼ to ⅓ cup of the cooled apple mixture in the center of each pastry round.
Fold each circle over the filling to form a half-moon shape. Press the edges together with your fingertips, then crimp or fold them again to create a secure seal.
Transfer the filled turnovers to the prepared baking sheet.
Using a sharp knife, make three small slits in the top of each turnover. These openings allow steam to escape during baking and help preserve the pastry’s crisp texture.
Crack the egg into a small bowl and beat it until evenly blended.
Lightly brush the surface of each turnover with the beaten egg. Distribute the granulated sugar generously over the coated pastry.
Bake for about 25 minutes, or until the turnovers are crisp and evenly golden brown.
Remove the baking sheet from the oven and allow the turnovers to cool for at least 15 minutes before serving.