Bring the apple cider to a boil in a medium saucepan over high heat. Cook until reduced to 1/2 cup, about 20 minutes. Remove from the heat and cool completely.
Preheat the oven to 450 degrees F.
In a large mixing bowl, combine the cooled cider, 1/3 cup sugar, cornstarch, lemon juice, vanilla, and pumpkin pie spice. Stir in the apple slices until evenly coated.
Roll one pie dough out into a large circle (large enough to fill the pie dish and slightly hang over the edge). Add apples and any liquid in the bowl to the crust. Roll out the top crust to the same size and place it on top of the apples.
Work your fingers around the outside edge of the pie crust to seal the edges together (you can crimp or use a fork as well). Cut six 1-inch vent slits into the top crust using a sharp knife.
Combine the egg and heavy cream in a small bowl. Brush the top crust and edges of the pie with the egg wash. Then sprinkle all over with 1 tablespoon sugar. Place the pie on a baking sheet. (It will catch any spills if the filling bubbles over.)
Bake on the center rack for 15 minutes. This will make the top of the crust very golden brown. Reduce the oven temperature to 350 degrees F and bake for another 60 minutes or until done.
Remove from the oven and cool the pie on a wire rack for 2-3 hours. (If the pie is cut when still warm the apple and juices will run all over. Letting it rest will allow the filling to thicken.)