Prepare: Preheat your oven to 425°F (220°C). Place one of the pie crusts into a 9-inch pie dish and press it gently into the bottom and up the sides.
Make the Filling: In a large bowl, toss the sliced apples with the granulated sugar, flour, cinnamon, nutmeg, and lemon juice until the apples are evenly coated.
Assemble the Pie: Pour the apple filling into the crust-lined pie dish. Scatter the small pieces of butter over the top of the filling.
Add the Top Crust: Place the second pie crust over the filling. Trim any excess crust from the edges. Crimp the edges of the top and bottom crusts together with a fork or your fingers to seal them. Cut a few small slits in the top crust to allow steam to escape.
Add Egg Wash: In a small bowl, whisk together the egg and 1 tablespoon of water. Brush this mixture lightly over the top crust. If using, sprinkle with coarse sugar.
Bake: Place the pie on a baking sheet (to catch any drips). Bake at 425°F (220°C) for 15 minutes. Then, reduce the oven temperature to 375°F (190°C) and continue to bake for another 35-40 minutes, or until the crust is deep golden brown and the filling is bubbly.
Cool Down (Crucial Step!): Let the pie cool on a wire rack for at least 2-3 hours before slicing. This allows the filling to set properly.