Whisk together the flour, salt, and sugar in a large mixing bowl.
Add the cold, cubed butter to the bowl.
Use a pastry cutter or your fingertips to blend until the mixture resembles coarse crumbs with pea-sized bits of butter.
Drizzle in the ice water one tablespoon at a time, gently mixing until the dough just comes together.
Divide the dough into two equal discs and wrap each in plastic wrap.
Refrigerate the dough for at least 1 hour to chill.
Once chilled, roll out one disc on a lightly floured surface into a 12-inch circle.
Fit the rolled dough into a 9-inch pie plate, leaving about a half-inch of overhang.
Place the lined pie dish in the refrigerator while preparing the filling.
Preheat the oven to 425°F.
Peel, core, and thinly slice the apples evenly.
Place the apples in a large bowl and add the brown sugar, granulated sugar, flour, cinnamon, nutmeg, cloves, allspice, lemon juice, and vanilla extract.
Toss the apple slices gently until fully coated in the mixture.
Let the apple mixture sit for 10 minutes to release some juice.
Roll out the second disc of dough for the top crust while the filling rests.
Remove the chilled bottom crust from the fridge.
Pour the apple filling into the prepared crust and spread it evenly, mounding it slightly in the center.
Dot the top of the filling with the diced butter pieces.
Place the rolled top crust over the apples or cut into strips to form a lattice design.
Trim excess dough, leaving about half an inch overhang, and fold it under the edge of the bottom crust.
Crimp the edges or press with a fork to seal.
Cut 4 to 5 small slits in the top if using a full crust to allow steam to escape.
In a small bowl, whisk together the egg and milk.
Brush the mixture over the top crust to create a golden finish.
Sprinkle coarse sugar evenly over the crust if desired.
Bake the pie at 425°F for 20 minutes.
After 20 minutes, reduce the oven temperature to 375°F and bake for an additional 35 to 40 minutes.
The pie is done when the crust is golden brown and the filling is bubbling through the lattice or vents.
If the edges brown too quickly, cover them loosely with foil during the final baking time.
Remove the pie from the oven and cool on a wire rack for at least 2 hours before slicing.
Serve warm or at room temperature for best texture and flavor.