Preheat your oven to 375°F (190°C).
Prepare the pastry dough by mixing flour, sugar, and butter in a large bowl until the mixture resembles coarse crumbs.
Stir in the beaten egg and vanilla extract, combining until the dough comes together. If too dry, add a teaspoon of cold water.
Divide the dough in half, wrap in plastic, and refrigerate for at least 30 minutes.
While the dough chills, prepare the apple filling by mixing sliced apples, brown sugar, cinnamon, lemon juice, and cornstarch in a separate bowl.
Roll out the dough on a floured surface to about ¼ inch thick and cut into circles to fit muffin tins.
Grease your muffin tin and gently press the dough circles into the wells to form the bases of the pies.
Spoon the apple mixture into each pastry cup, filling them almost to the top.
Roll out the remaining dough and cut smaller circles or strips for the tops. Lay them over the filling and crimp edges to seal.
Brush the tops with additional beaten egg for a golden finish.
Bake in the preheated oven for 25-30 minutes, or until the tops are golden brown.
Remove from the oven and let cool slightly before serving.