Start by peeling and slicing the apples into thin pieces. Place them in a large bowl. Add lemon juice to keep the apples fresh and bright. This step also adds a little tangy flavor that balances the sweetness of the pie filling.

Add granulated sugar, brown sugar, flour, cinnamon and nutmeg to the apples. Stir gently until all apple slices are coated evenly. The sugar mixture will slowly draw out natural juices from the apples, creating a delicious filling.

Place one pie crust into the pie dish. Press it gently along the bottom and sides. Make sure the crust fits smoothly without tearing. This crust will hold the apple filling and create the base of the pie.

Pour the apple mixture into the prepared crust. Spread it evenly so the apples cook properly. Place small cubes of butter over the apples. Butter melts during baking and adds a rich flavor to the filling.

Place the second pie crust over the apple filling. Trim the edges and pinch them together to seal. Use a knife to cut small slits on the top crust. These slits allow steam to escape while baking.

In a small bowl, mix the egg and milk. Brush this mixture over the top crust using a pastry brush. The egg wash helps the crust turn golden and shiny during baking.

Preheat the oven to 375°F (190°C). Place the pie on a baking tray to catch any drips. Bake for about 40 minutes. The crust should turn golden brown and the filling should bubble gently.

Remove the pie from the oven and allow it to cool for at least 20 minutes. Cooling helps the filling thicken slightly. This makes slicing easier and keeps the pie neat.

Cut the pie into even slices using a sharp knife. Serve warm for the best flavor. Many people enjoy apple pie with vanilla ice cream or whipped cream.