Preheat the oven to 425°F. In a large mixing bowl, toss the apple slices with the lemon juice. Add the sugar, flour, and spices. Stir until the apples are well coated. On a lightly floured surface, roll one disc of pie dough into a 12-inch to 14-inch circle. Line a 9-inch pie pan with the dough, letting the excess hang over the edge. Pour the apple filling into the crust and pat it into an even layer, mounding it slightly in the center. Dot with the butter. Roll the second pie dough into roughly an 11-inch circle (about ⅛-inch thick). Place on top of the filling for a solid top, or cut the dough and arrange in the desired pattern. Trim the excess pie dough to about an inch from the edge of the pie plate, tuck the excess under and crimp the edges as desired. Cut slits in the top of the pie to create steam vents if covered with a solid top crust. Place on a rimmed baking sheet. Brush the crust with the beaten egg and sprinkle with additional sugar, if desired. Bake for 20 minutes. Reduce the heat to 375°F and continue baking until the crust is a deep golden brown and the filling is bubbly, about 50 minutes to 1 hour. (If the crust browns too quickly at any point, loosely cover the whole pie or the edges with foil.) Let cool completely on a wire rack, about 4 hours before slicing.