In a large mixing bowl, combine the flour and a pinch of salt. Add the cold, cubed butter and use a pastry cutter or fork to cut the butter into the flour until the mixture resembles coarse crumbs with pea-sized pieces. Gradually add ice water, mixing lightly until the dough begins to come together. Form into two equal disks, wrap in plastic wrap, and refrigerate for at least 30 minutes.
Preheat the oven to 375°F (190°C). Peel, core, and slice the apples thinly. Toss the apple slices in lemon juice, sugar, and cinnamon until evenly coated. Set aside to allow flavors to meld.
2 cups all-purpose flour
On a lightly floured surface, roll out one of the chilled dough disks into a 12-inch circle. Transfer it to a greased 9-inch pie dish, gently pressing into the bottom and sides. Pour the apple filling into the pie crust, mounding slightly in the center.
2 cups all-purpose flour
Roll out the second dough disk to the same size, then place it over the filled pie. Trim excess dough and crimp edges to seal. Cut small vents in the top crust to allow steam to escape. Mix the beaten egg with milk to create an egg wash and brush it over the top crust for a golden finish.
2 cups all-purpose flour
Bake the pie in the preheated oven for about 45 minutes, or until the crust is golden brown and the filling is bubbling through the vents. During baking, the apple filling will soften and caramelize, creating a glossy, fragrant top.
Let the pie cool for at least 15 minutes before slicing. Serve warm or at room temperature to enjoy the tender apples encased in flaky pastry.
