Preheat your oven to 425°F. Place a rimmed baking sheet on the lower rack to catch any bubbling juices and help the bottom crust bake evenly.
In a large bowl, toss the sliced apples with lemon juice.
Add the granulated sugar, brown sugar, flour, cinnamon, nutmeg, and ginger. Stir until the apples are evenly coated and glossy.
Roll out one pie crust and fit it into a 9-inch pie dish. Let the excess hang over the edges for now.
Spoon the apple filling into the crust, packing it in gently so there are fewer air pockets. Dot the top with the butter pieces.
Roll out the second crust and place it over the filling. Trim the extra dough, tuck the edges under, and crimp or pinch them to seal. Cut several slits in the top if you’re using a full crust.
Whisk the egg with the milk and brush it over the top crust. Sprinkle with coarse sugar if desired.
Bake for 20 minutes at 425°F, then reduce the oven temperature to 375°F and bake for 45 to 55 minutes more, until the crust is deep golden brown and the filling is bubbling.
Cool the pie completely on a wire rack for at least 3 to 4 hours before slicing.