Preheat oven to 375℉. Place the oven rack in the lower third of the oven. Place baking a baking sheet on the rack before preheating the oven.
Line the pie pan with one crust. Cover with plastic wrap and chill until the apple filling is ready. Wrap the other crust in plastic wrap and chill.
Place the apple slices, cinnamon, nutmeg, light brown sugar and granulated white sugar into a large mixing bowl. Mix well to coat all apples.
In a small saucepan, melt the butter, pour over filling and mix well.
Pour the apple filling into the chilled pie crust lined pan.
Gently place the top crust on top. Seal around the edge. If needed, use kitchen shears to trim the overhang to one inch around (extra dough can be used to make a decorative leaf on top). Crimp edges. Using a sharp knife, make 5 or 6, 2-inch slits from the center of the pie out towards the edge to allow for steam to be released as the pie bakes.
In a small bowl, whisk the egg and water. Brush the top of the pie with the egg wash. Sprinkle with granulated sugar.
Place the pie on the heated baking sheet on the lower third of the oven.
Bake for about 50 minutes. The pie is done when the top is golden brown and the juices bubble through the steam slits. If it looks like the edges or top of the pie is browning too fast, cover with aluminum foil.
Place the pie on a wire rack to cool. For optimal results, let the pie cool for at least 4 hours. Serve warm or at room temperature with vanilla ice cream or whipped cream.