Preheat your oven to 220°C (425°F). Set aside a 9-inch pie plate.

In a large pot over medium-low heat, melt the butter. Add the sliced apples, brown sugar, flour, cinnamon, lemon juice, and salt. Stir everything together and cook, stirring occasionally, until the apples soften, about 8 to 10 minutes. Remove from heat and let the mixture cool.

If you have prepared pie dough in two discs, sprinkle flour on a clean surface. Roll one disc out to about 0.3 cm (1/8 inch) thick, making it slightly larger than your pie plate. Carefully transfer it into the pie plate, pressing gently to fit.

In a small bowl, whisk together the egg and water to create an egg wash.

Once the apple mixture has cooled, transfer it into the prepared pie crust.

Roll out the second disc of pie dough on a floured surface and place it over the apple filling. You can cut the dough into strips and create a braided pattern if you like, or cut vents in the crust. Trim any excess dough hanging from the edges and crimp them with your fingers to seal.

Lightly brush the top of the pie with the egg wash. If desired, sprinkle coarse sugar over the top for added sweetness and texture.

Bake the pie for 15 minutes at 220°C (425°F). After that, reduce the temperature to 175°C (350°F) and continue baking until the top is golden brown, and the apple filling bubbles through the vents, about 40 minutes. If the crust starts to brown too much, cover it loosely with aluminum foil.

Once baked, set the pie aside to cool before slicing and serving.