Prepare the Apple Filling: Begin by peeling, coring, and dicing the apples into small cubes. Combine the apples with the brown sugar, cinnamon, and vanilla in a medium saucepan over medium heat. Cook for about 3 minutes, allowing the apples to release their juices.

Thicken the Filling: In a small bowl, whisk together the apple cider (or juice) and cornstarch. Stir this mixture into the apple filling. Increase the heat and cook for another 3 minutes, stirring continuously until the mixture thickens. Remove from heat and set aside to cool.

Make the Pie Dough: In a large bowl, sift the flour. Cut the cold, cubed butter into the flour using a pastry cutter until it forms small, pea-sized pieces. In a separate bowl, whisk together the egg yolks and salt. Heat the milk in the microwave until hot, then slowly pour it into the egg mixture, stirring constantly. Gradually mix this into the flour mixture to form a dough.

Knead the Dough: Transfer the dough onto parchment paper and knead briefly for about a minute, until it becomes smooth. Divide the dough into 6 equal pieces, rolling each into a ball. Roll out each ball into a circle using a rolling pin.

Fill and Shape the Pies: Spoon 2 tablespoons of the apple filling onto one side of each dough circle. Fold the dough over to form a semi-circle, pressing the edges to seal. Use a fork to crimp the edges, ensuring the filling is sealed inside. If desired, trim the excess dough with a pastry cutter or knife.

Fry the Pies: Heat oil in a deep fryer or heavy pan to 350°F. Gently lower each pie into the hot oil, frying for about 2 minutes on each side, or until golden brown. Transfer the fried pies to a paper towel-lined plate to drain excess oil.

Glaze the Pies: While the pies are still warm, prepare the glaze by whisking together the powdered sugar, milk, and vanilla until smooth. Use a pastry brush to coat each pie with the glaze, or dip the pies into the glaze.

Serve: Allow the glaze to set briefly, then enjoy your fried apple pies warm for the best flavor.