Preheat your oven to 220°C (425°F).

In a large bowl, mix the flour, salt, and sugar together. Cut in the cold diced butter until the mixture resembles coarse crumbs.

Stir in enough ice water until the dough starts to form a ball.

Divide the dough in half, shape each half into discs, wrap them in plastic wrap, and refrigerate for at least 4 hours or overnight.

Once chilled, roll out one disc on a floured surface. Fit it into a pie dish.

In another bowl, mix the sliced apples with sugar, cinnamon, and lemon juice. Pour this filling into the rolled crust and dot the top with small pieces of butter.

Roll out the second disc of dough and place it over the apple filling. Seal the edges by crimping them with a fork or your fingers. Cut slits in the top to allow steam to escape.

Brush the top of the pie with beaten egg to give it a beautiful shine when baked.

Bake for 15 minutes at 220°C (425°F), then reduce the temperature to 175°C (350°F) and continue baking for 35-45 minutes until the crust is golden brown.

Allow the pie to cool before serving it warm.