Preheat oven to 425°F. Prepare the pie crust and roll out a bottom crust to be slightly larger than a 9-inch pie plate. Use it to line the pie plate.
In a large bowl, toss the peeled, cored, and sliced apples with the lemon juice to help prevent them turning brown. Sprinkle the sugar, flour, cinnamon, nutmeg and salt over the apples and toss to combine. Let sit for 15 minutes to draw out juices.
Spread apples into dough-lined pie plate, mounding them in the middle. If there is a lot of juice left in the bowl, microwave it for 2 minutes until it reduces and thickens somewhat, then add it to the apple pie filling. Dot with 1 tablespoon of butter that has been cut into small cubes.
Roll out the pie crust and transfer it to cover the pie filling. Trim overhanging pie crust dough to ½ inch beyond lip of pie plate. Tuck the overhanging crust under itself so it is flush with edge of pie plate, then crimp the dough using your thumb and forefingers.
Cut slits in top of dough to allow the pie to vent as it bakes. Brush the top crust with the beaten egg using a pastry brush.
Place the apple pie on a baking sheet to catch any juices that might bubble out as the pie cooks, then place in the preheated oven and bake for 25 minutes. Reduce the heat to 375°F and continue to cook another 30-35 minutes until the crust is a deep golden brown color. I always place a pie crust shield around the edges of the pie at this point.
Let the pie cool completely (about 4 hours) before slicing and serving.