Mix flour, salt, and sugar together. Cut in the cold butter until crumbly.
Add ice water slowly until dough forms. Divide dough into two equal portions.
Wrap each portion in plastic wrap tightly. Refrigerate for at least 30 minutes.
Peel and slice all the apples thinly. Combine apples with both sugars in bowl.
Add flour, cinnamon, and nutmeg to mixture. Pour lemon juice over the apples evenly. Toss everything together until well coated.
Roll out one dough portion for bottom. Place it in your pie dish carefully.
Add the apple filling on top evenly. Dot the filling with butter pieces throughout.
Roll out second dough for top crust. Cover the pie and seal the edges. Cut small slits on top for venting.
Preheat your oven to 375°F first. Brush pie crust with egg wash lightly.
Bake for 50 to 55 minutes total. The crust should turn golden brown nicely. Let the pie cool completely before slicing.