Combine apples, sugars, four, vinegar, vanilla, cinnamon, nutmeg, and salt in a large mixing bowl. Let sit while rolling out the pie crusts.
Remove the crusts from the refrigerator and let sit for about 10 minutes. Roll one of the doughs out between two sheets of waxed or parchment paper into a 12-inch circle. Transfer to a 9-inch pie pan and crimp the edges.
Stir apples and spoon into the pie crust. Roll the second pie crust between two sheets of waxed or parchment paper into an even thickness of about ¼ inch. Cut out the dough into shapes using large cookie cutters (smaller shapes tend to brown too fast) and layer on top of the apple filling. Brush the top with beaten egg and sprinkle with coarse sugar. Refrigerate the pie for 30 minutes.
Preheat oven to 400°F. Bake pie for 20 minutes then reduce the oven temperature to 350°F and bake another 40 minutes or until the filling is bubbly and the crust is golden brown. If the crust is browning too fast, tent loosely with foil.