Preheat the Oven: Preheat your oven to 375°F (190°C). Place a baking sheet on the middle rack to catch any drips from the pie.
Prepare the Filling: In a large mixing bowl, combine the sliced apples, granulated sugar, flour, cinnamon, nutmeg, and lemon juice. Toss until the apples are evenly coated with the sugar and spices.
Assemble the Pie: Roll out one pie crust and gently place it into a 9-inch pie dish, allowing the edges to hang over the sides. Spoon the apple filling into the crust, spreading it out evenly. Dot the top of the filling with small pieces of butter.
Top and Seal the Pie: Roll out the second pie crust and place it over the filling. Trim any excess dough from the edges, leaving about a 1-inch overhang. Fold the overhang under the bottom crust and crimp the edges to seal. Cut a few slits in the top crust to allow steam to escape.
Brush with Egg Wash: Brush the top crust with the beaten egg, then sprinkle evenly with the remaining tablespoon of granulated sugar.
Bake the Pie: Place the pie on the preheated baking sheet in the oven and bake for 45-50 minutes, or until the crust is golden brown and the filling is bubbly. If the edges of the crust start to brown too quickly, you can cover them with aluminum foil halfway through baking.
Cool and Serve: Remove the pie from the oven and allow it to cool on a wire rack for at least 2 hours before serving. This will allow the filling to set and prevent it from being too runny when sliced. Serve slices of apple pie warm or at room temperature, optionally with a scoop of vanilla ice cream or a dollop of whipped cream.