Combine all-purpose flour, granulated sugar, and salt in a large mixing bowl. Cut in cold unsalted butter until the mixture resembles coarse crumbs. Gradually add ice water, mixing until the dough comes together. Divide the dough in half, shape into discs, wrap in plastic wrap, and refrigerate for at least 1 hour to chill.

While the dough chills, wash, peel, and slice the apples into thin pieces. Toss apple slices with granulated sugar, brown sugar, cinnamon, nutmeg, lemon juice, and cornstarch until evenly coated. Let sit for about 15 minutes.

Preheat your oven to 425°F (220°C). Roll out one disc of the chilled dough into a 12-inch circle. Transfer to a 9-inch pie dish, pressing gently. Trim excess dough.

Spoon the apple filling into the prepared pie crust. Roll out the second disc of dough, cut into strips, and create a lattice pattern over the filling. Trim and crimp the edges to seal the pie.

Brush the lattice crust with egg wash. Sprinkle dark brown sugar generously over the lattice.

Place the pie on a baking sheet and bake for 45–50 minutes. Cover edges with foil if necessary during the last 15 minutes to prevent over-browning.

Remove pie from the oven and let it cool on a wire rack for at least 2 hours before serving.