1. In a large bowl, combine flour and salt. Cut in the cold butter using a pastry cutter or food processor until the mixture resembles coarse crumbs. Gradually add ice water, one tablespoon at a time, until the dough forms. Divide and chill for at least 1 hour.

2. Toss sliced apples with lemon juice, both sugars, flour, cinnamon, nutmeg, and a pinch of salt. Let the mixture sit for 20 minutes.

3. Roll out one chilled dough disc into a 12-inch circle. Fit into a 9-inch pie dish. Roll the second disc for the top crust or lattice.

4. Fill the pie shell with apple mixture. Dot with butter. Cover with top crust, crimp edges, and cut vents or create lattice.

5. Brush the top with beaten egg and milk. Sprinkle with coarse sugar if using.

6. Bake at 400°F (200°C) for 20 minutes, then reduce to 375°F (190°C) and bake for another 35–40 minutes, until the crust is golden and the filling bubbles.

7. Cool on a wire rack for at least 2 hours before slicing.