Mix flour and salt in a large bowl. Add your chilled butter cubes and use a pastry cutter or fork to break them into pea-sized pieces. This takes about 3 minutes—don't rush it. You'll see little butter flecks throughout. Add ice water one tablespoon at a time, mixing gently until dough just comes together. Chill for 30 minutes minimum.
Divide dough in half and roll one half between parchment paper until it's about 1/8-inch thick. Transfer to a 9-inch pie dish. Trim edges, then chill for 15 minutes while you prep the filling. Roll the second half for your top crust and chill it separately.
Toss your sliced apples with both sugars, cinnamon, nutmeg, and lemon juice in a large bowl. Let this sit for 5 minutes—you'll hear the mixture start to bubble slightly as the sugar dissolves and creates juice. This is exactly what you want. The apples will soften just enough without getting mushy.
Preheat your oven to 425°F. Pour the apple mixture into your chilled crust, mounding slightly in the center. Don't worry if there's liquid in the bottom of the bowl—pour about half of it over the apples. Save the rest for later.
Place your second crust on top and seal the edges by pressing them together with a fork. Cut 4 small slits in the top for steam to escape. Mix egg and milk together, then brush this egg wash over the entire top crust. Sprinkle a pinch of cinnamon sugar on top if you're feeling fancy.
Bake at 425°F for 20 minutes, then reduce heat to 375°F and bake for 30 more minutes. When your kitchen smells like caramelized cinnamon and buttery apples—that's your signal the filling is done. The crust should be deep golden brown, not just light tan. If edges brown too fast, cover them loosely with foil.
Remove from oven and let cool on a wire rack for at least 2 hours before slicing. I know it's torture to wait, but cutting into a warm pie makes it fall apart. After 2 hours, it holds together beautifully. The filling sets up and the crust firms up enough to slice cleanly without crumbling everywhere.