Add the peeled, cored and sliced apples to a large mixing bowl. If apples lack tartness, sprinkle with 1 tablespoon fresh lemon juice. In a small bowl, whisk together the sugar, flour, cinnamon and nutmeg. Add the sugar mixture to the sliced apples; toss to coat the fruit. Set aside.
Preheat oven to 375 degrees F.
Remove the pastry from the refrigerator and allow it to sit at room temperature about 15 minutes. Roll out one disc of the dough on a lightly floured, clean work surface to a 12-inch circle. Gently fit the pastry dough into a deep dish 9-inch pie plate taking care not to stretch the dough. Trim the edges of the dough leaving about a 1-inch overhang.
Fill the pastry with the apple mixture; dot with the remaining 2 tablespoons of diced butter. Roll out the remaining disc of dough and fit over the apples. To seal the edges, use a wet finger to moisten the edge of the pie crust (around the rim.) Fold the trimmed top crust edge over and under the edge of the bottom crust. Press to seal then flute the edge in a decorative pattern. Cut two or three small slits in the top crust to vent. If desired, roll out the scraps of dough and cut into decorative designs using cookie cutters or a small knife. Lightly brush the top of the pie with the egg/milk mixture. Discard the remaining egg mixture as you will not use it all. Sprinkle the top of the pie with sugar if desired.
Line the bottom rack of your oven with a large piece of foil in case juice bubbles out of the pie while baking. Bake at 375 degrees F for at least 1-hour, and up to 1-hour and 15-minutes depending on the height and thickness of the pie. The filling should be bubbly and the crust a golden brown. When checking the pie, you should be able to hear it bubbling inside the crust. If the crust is over-browning during baking, tent with foil. Remove to a rack to cool.
Serve with a slice of cheddar cheese or ice cream if desired. Pie should keep lightly covered at room temperature for up to 3 days. Refrigerate leftovers if desired for longer storage.