Pour the apple filling into the prepared bottom crust, mounding it slightly in the center.
Dot the top of the filling with small pieces of unsalted butter.
Roll out the second portion of chilled dough on a lightly floured surface into a circle slightly larger than the pie dish.
Carefully place the rolled-out dough over the filling. Trim any excess dough hanging over the edges, leaving about a 1-inch overhang.
Fold the overhang of the top crust under the edge of the bottom crust, then crimp the edges using your fingers or a fork to seal the pie.
Use a sharp knife to create several small slits or decorative vents in the top crust to allow steam to escape during baking.
Brush the top crust with the beaten egg, then sprinkle evenly with granulated sugar for a golden finish.
Place the pie in the preheated oven and bake for 45-50 minutes, or until the crust is golden brown and the filling is bubbling and thickened.
Remove the pie from the oven and let it cool on a wire rack for at least 2 hours before slicing and serving.
Serve the apple pie warm or at room temperature, optionally topped with a scoop of vanilla ice cream or a dollop of vanilla yogurt.