Preheat the oven to 425°F (220°C).
In a mixing bowl, combine the flour, salt, and sugar for the crust. Add the cold diced butter and mix until the mixture resembles coarse crumbs.
Add the ice water, one tablespoon at a time, mixing until the dough forms a ball. Chill the dough in the refrigerator for at least 15 minutes.
In another bowl, combine sliced apples, granulated sugar, cinnamon, nutmeg, lemon juice, and flour for the filling. Set aside.
Roll out the chilled dough on a floured surface to fit the 9-inch pie pan. Place it in the pan and trim the edges.
Pour the apple filling into the crust, spreading it evenly.
In a separate bowl, prepare the crumb topping by mixing flour, brown sugar, softened butter, cinnamon, and salt until crumbly. Evenly sprinkle the topping over the apple filling.
Bake the pie in the preheated oven for 15 minutes at 425°F, then reduce the temperature to 350°F (175°C) and continue baking for 45 minutes, or until the apples are tender and the topping is golden brown.
Allow the pie to cool for at least 15 minutes before serving. This will help the filling set.
Serve warm with vanilla ice cream or whipped cream for added deliciousness.