In a large bowl, mix flour, salt, and sugar. Add cold butter cubes and rub until crumbly. Slowly add ice water and form dough, then chill for 30 minutes before using.

Peel and slice apples evenly into thin pieces. Place in a bowl and add lemon juice. Toss gently so apples stay fresh and do not brown while you prepare filling.

Add sugar, brown sugar, cinnamon, nutmeg, flour, and vanilla to apples. Mix gently until fully coated. The mixture should smell warm, sweet, and well balanced with spice and fruit flavor.

Divide chilled dough into two parts. Roll one portion into a circle on a floured surface. Make sure it is large enough to fit pie dish with extra edges for sealing.

Place rolled dough into pie dish carefully. Press gently into corners and edges. Let extra dough hang over sides. This helps seal the pie later and keeps filling inside while baking.

Pour apple mixture into prepared crust. Spread evenly and slightly mound in center. This helps create a full, bakery style pie that looks beautiful after baking and slicing later.

Roll second dough piece and place over filling. Trim extra edges and seal tightly. Crimp edges with fork or fingers to lock filling inside and create a neat finished pie shape.

Brush top with egg and milk mixture, then sprinkle sugar. Cut small slits for steam. Bake at 375°F for 45 to 50 minutes until golden brown and filling is bubbling.

Remove pie from oven and let it cool for at least 20 minutes. This helps filling set properly. Slice carefully and serve warm for best texture, flavor, and comforting experience.