1. Preheat your oven to 375°F (190°C) and line a rimmed baking sheet with parchment paper.
2. In a large bowl, combine the flour, salt, and sugar. Add the chilled butter and use a pastry cutter or your fingers to work it into the flour until the mixture resembles coarse crumbs.
3. Drizzle in the ice water, a tablespoon at a time, and mix until the dough begins to come together. Divide the dough in half, shape into discs, wrap in plastic, and refrigerate for at least 30 minutes.
4. While the dough chills, prepare the filling by tossing the apples with granulated sugar, brown sugar, cinnamon, nutmeg, flour, and lemon juice.
5. Roll out one disc of dough on a floured surface to fit the baking sheet. Transfer the dough to the prepared sheet.
6. Spread the apple mixture over the dough, leaving a small border around the edges. Dot with butter.
7. Roll out the second disc of dough and place it over the apple filling. Seal the edges by crimping with a fork or your fingers, and cut small slits on top to allow steam to escape.
8. Brush the top crust with the beaten egg and sprinkle with coarse sugar if desired.
9. Bake for 40-45 minutes or until the crust is golden brown and the filling is bubbly. Let the pie cool slightly before slicing and serving.

Remember, as my grandmother taught me, don’t stress about perfection. It’s the love and care you put into each step that truly counts.