Pre-heat the oven to 425 ̊F.

Roll out the pastry circles on a floured surface until they are about ¼-inch thick. Place one circle of rolled out dough into the pie dish and gently press the dough into the edges of the dish. Trim the edges of the pastry and refrigerate the pie shell for 30 minutes. Place the other circle of dough in the refrigerator, either rolling it up in parchment paper or a silicone baking sheet.

Combine the apples, sugars and spices in a large bowl and toss together. Let this sit and macerate for at least 30 minutes. Strain the apples through a colander into a bowl, reserving the liquid. Bring this liquid to a simmer in a small saucepan on the stove and reduce it almost by half.

Toss the apples with the cornstarch and then return the reduced liquid to the mix. Transfer the apples to the pie dish with the rolled out pastry. Pile the apples high in the dish and dot the apples with the butter. Drape the remaining rolled out pastry circle over the top.

Brush the lower edge of the pastry with water, and seal the top edge of the pastry down on the bottom edge. Once sealed together, trim the pastry around the dish. Make 5 or so slits or cut outs in the pastry to allow steam to escape during cooking. Brush the surface of the pie with the lightly beaten egg, and sprinkle the surface with sugar.

Bake in the oven for 30 minutes. Reduce the heat to 350 ̊ F and continue to bake for another 20 to 25 minutes. If at any point the edges of the crust are getting too dark, cover the edges with aluminum foil. The pie is finished when nicely browned on top and the apples inside are tender and soft when pierced with a paring knife through one of the vent slits.