In a mixing bowl, combine flour and salt. Add chilled butter and mix until the mixture resembles coarse crumbs.

Stir in ice water, a tablespoon at a time, until the dough comes together. Divide the dough in half, shape into discs, wrap in plastic, and refrigerate for at least 1 hour.

In a large bowl, toss sliced apples with sugar, lemon juice, cinnamon, nutmeg, and flour until well combined.

Preheat the oven to 425°F (220°C). Roll out one disc of dough on a floured surface to fit the pie dish. Place the rolled dough in the pie dish.

Fill with the apple mixture and dot with butter. Roll out the second disc of dough and place over the filling. Seal and flute the edges, then cut slits in the top crust for steam to escape.

Bake in the preheated oven for 15 minutes. Reduce the temperature to 350°F (175°C) and continue baking for 30-35 minutes, or until the apples are tender and the crust is golden brown.

Let the pie cool before serving.