Make the Crust
Add flour, sugar, and salt to a large bowl.
Cut cold butter into the flour until it looks like coarse crumbs.
Add ice water one tablespoon at a time until dough comes together.
Divide dough into two discs, wrap, and chill for at least 30 minutes.
Prepare the Filling
Preheat oven to 425°F (220°C).
In a large bowl, toss apples with sugars, lemon juice, cinnamon, nutmeg, salt, and cornstarch until evenly coated.
Assemble the Pie
Roll out one dough disc and fit it into a 9-inch pie dish.
Fill with apple mixture and dot with butter.
Roll out second dough disc and place on top. Seal and crimp edges.
Cut small slits in the top crust for ventilation.
Brush with egg wash and sprinkle with coarse sugar if using.
Bake
Bake at 425°F for 15 minutes.
Reduce temperature to 375°F (190°C) and bake for 40–50 minutes, until crust is golden and filling bubbles.
Cool
Let pie cool for at least 2 hours before slicing.