Preheat oven to 375°F (190°C).
Prepare the pie crust by mixing flour, salt, and sugar. Cut in cold butter until mixture resembles coarse crumbs. Add ice water, a tablespoon at a time, until dough comes together. Divide dough in half and shape into discs. Wrap in plastic wrap and chill for 30 minutes.
Roll out one disc of dough on a floured surface and fit into a 9-inch pie dish.
In a bowl, mix sliced apples with sugar, cinnamon, nutmeg (if using), and lemon juice.
Pour apple mixture into prepared pie crust.
Roll out the second disc of dough and place it over the apple filling. Trim excess dough and crimp edges to seal.
Cut slits in the top crust to allow steam to escape.
Place pie on a baking sheet to catch any drips and bake for 45-55 minutes, or until crust is golden and filling is bubbly.
Cool on a wire rack for at least 30 minutes before serving.
Serve warm with ice cream or whipped cream, if desired.