In a medium-sized mixing bowl, whisk together the flour, sugar, and salt. Add the diced butter, and use a pastry blender to cut it into the flour mixture until the butter forms small, pea-sized clumps throughout.

Gradually add ice water, one tablespoon at a time, tossing the mixture until it begins to come together in larger clumps. Gather the dough into a ball, then press and shape it into a smooth, 6-inch round disk on a lightly floured surface. Cover the dough and refrigerate for about 60 minutes until it becomes firmer.

After chilling, roll out the dough on a lightly floured surface into a 12 1/2-inch circle. Carefully fold the dough in half, then into quarters, or wrap it around a rolling pin to transfer it to a 9 to 9 1/2-inch deep-dish pie plate. Unfold the dough and fit it to the pie plate, crimping the edges if desired.

Refrigerate the dough for about 1 hour to chill thoroughly (or freeze it for 15 minutes). Meanwhile, preheat your oven to 400°F (200°C). Line the crust with a sheet of foil or parchment paper, ensuring it covers the edges, and fill it with pie weights, dry beans, rice, or sugar, leveling it to the top. Bake the crust in the preheated oven for 15 minutes.

Carefully remove the foil and weights, then prick the bottom of the crust with a fork about 10 times. Return the crust to the oven and bake for an additional 8 to 12 minutes, until it begins to dry out. Once baked, remove the crust and let it cool on a wire rack while you prepare the crumb topping and apple filling.

Reduce the oven temperature to 350°F (175°C) and lower the oven rack by one level from the center.

In a medium mixing bowl, break up the brown sugar with your fingertips, then whisk in the flour, ground nutmeg, and salt.

Pour the vanilla extract into the melted butter and stir. Add this butter mixture to the flour mixture, tossing until evenly moistened. Place the topping in the refrigerator while you work on the filling.

In a large mixing bowl, toss the sliced apples with the melted butter and fresh lemon juice. Sprinkle the granulated sugar, flour, and cinnamon over the apples, then toss until the slices are evenly coated.

Layer the apple mixture into the prepared pie crust, adding a handful or two at a time. Press and spread the apples into an even layer, making sure the slices lay flat, which will help fit all of them in.

Retrieve the crumb topping from the refrigerator, break it into small clumps, and sprinkle it evenly over the apple filling.

Place the assembled pie on a rimmed baking sheet, and bake it in the preheated oven for 45 to 55 minutes, or until the apples are nearly tender when tested with a toothpick. Keep an eye on the pie during baking, checking to ensure the topping or crust isn't browning too quickly. If necessary, tent the pie with foil. If the pie isn't browning enough, you can move the oven rack up one level.

Once baked, remove the pie from the oven and allow it to cool on a wire rack for about 2 hours. Serve the pie slightly warm, with a scoop of vanilla ice cream if desired.