Bring cider to a boil in a large, heavy saucepan over medium high heat. Once it comes to a boil, reduce heat as much as possible to maintain a simmer. Cook until reduced to ½ to ⅓ cup (about 20 minutes). You know it's done when you can scrape the bottom of the pan with a flat wooden spoon and it takes a second for the reduced cider to cover it back up. Cool completely.
Preheat oven to 450° F with a baking sheet on a rack that is in the lower third of the oven.
Combine cooled cider, ⅓ cup sugar, cornstarch, lemon juice, vanilla, and pumpkin pie spice in a large bowl. Stir apple slices into cider mixture.
Fit dough into a 9-inch pie plate, allowing dough to extend over edge of plate. Spoon apple mixture into crust. Place second pie crust on top of apple mixture. Dip finger into small bowl of water, rub along edges of pie crust, then gently press edges of dough together to seal. Fold edges under and flute.
Cut several slits into the top of pastry using a sharp knife to allow steam to escape during the cooking process. Combine egg and 1 teaspoon of water. Brush top and edges of pie with egg mixture, then sprinkle with sugar.
Place pie on preheated baking sheet, and bake at 450° for 15 minutes. Reduce oven temperature to 350° (do not remove pie from oven), and bake an additional 45-60 minutes (see note below) or until golden brown. Cool on a wire rack.