Preheat oven to 425°F.
Make pie crust as directed. Divide into two equal pieces. Roll half of dough into a 12-inch circle (about ⅛-inch thickness) and place in a 9-inch pie plate (not deep dish). Roll out the second piece of dough to a 12 inch circle between sheets of wax paper. Chill both crusts until ready to use. (See notes for link to pie crust tips).
Place the apples and 1 cup of apple cider in a large skillet. Cover and cook over medium heat, stirring often, until the apples are almost translucent, about 5-7 minutes. Remove the apples and reserve the cooking liquid in the pan.
Stir together granulated sugar, 1 tablespoon cornstarch, and salt. Stir in remaining 2 tablespoons of cold apple cider. Add the cornstarch mixture to the hot apple liquid in the pan. Cook over medium-low heat until the mixture thickens, about 5 minutes. Add the butter and stir until melted. Remove from heat and add the apples back to the hot liquid. Let cool for 5-10 minutes.
Remove crusts from the refrigerator. Remove wax paper from top crust. At this point you can make a lattice, do a decorative crust, or just make a two crust pie. The pie shown in the photos is a decorative crust that uses small square cookie cutters to make it look like lattice. Prepare top crust as desired.
Sprinkle the brown sugar, cinnamon and remaining 1 teaspoon cornstarch in the bottom of the pie crust in the pie plate. Place the slightly cooled apples into the pie plate.
Top carefully with top crust. Crimp edges. (If not using a lattice or decorative pattern, be sure to cut slits in the top crust for air to escape.)
Brush the top of the pie with egg wash. Place the pie on a cookie sheet and top with a pie crust shield.
Bake at 425°F for 15 minutes then lower the oven temperature to 350°F and cook until crust is golden and baked through and filling is bubbly (approximately 30-40 additional minutes). If the top browns too quickly you can tent the pie with foil. Remove pie crust shield after about half the bake time.
Cool completely before slicing (chilling will help set the pie). Serve room temperature or warm plain or with ice cream.