Put the apples in a bowl and mix in the lemon juice, sugar, cinnamon, nutmeg, and cornstarch. Let it sit for 15 minutes to release water.
Transfer the filling mixture to a sauce pan and reduce the liquid over medium to low heat for around 15 minutes, stirring regularly. Then turn off the heat.
While the filling is sitting/reducing, start the crust by putting the flour, salt, sugar, and pieces of butter in a food processor.
Run the food processor until it resembles a coarse sand (5-10 seconds), then start dripping in the ice water until the mixture starts to chunk together. You'll know it's done if you can pinch the dough and it sticks together.
Preheat oven to 350°F.
Cut the dough in half and roll both halves out with a rolling pin until they are big enough to cover your pie pan (around 9 inch diameter).
Put the bottom half dough into the pie pan and cut off the excess dough with a knife.
Dump the filling into the pie pan and even it out.
Cover the pie filling with the top dough and fold over and tuck in the excess crust.
Use a fork or your fingers to pinch down the top crust to the bottom crust so you don't have air gaps.
Optionally brush on the egg wash for a shiny golden brown crust.
Cut a few slits in the top crust for a nice design and to allow air to release.
Bake 45 minutes at 350°F or until the crust is brown to your liking and the apples are bubbling inside.