To make the pie crust and decorative top: On a lightly floured surface, roll one of the dough disks into a 12-inch round that's 1/8 inch thick (trim an edge to check the thickness). Fold the dough in half, ease it into a 9-inch pie pan, and unfold it. Press the dough up the sides and over the rim of the pan, and trim it to the outer edge. Chill the dough while you cut out the leaves.
Pat the scraps into the bottom of the second disk and roll out the dough to 1/8 inch thick (the shape doesn't matter). With a paring knife or a leaf cutter, cut out as many 2x1-1/2 inch leaves as you can, veining them with the dull edge of a paring knife, if you like. Pat the scraps together, roll out the dough again, and cut out more leaves. You'll need 45 to 55 leaves to cover the pie. (You can make smaller or larger leaves, if you like; you'll need more or fewer leaves accordingly.) Set the leaves aside in a cool place (but not in the refrigerator).
Cut out as many leaves as you can with a paring knife.
Vein the leaves with the dull side of the knife. Use gentle but steady pressure to indent each leaf, pressing just less than halfway through the dough.
To make the filling and bake: Peel, quarter, and core the apples. Cut them into 1/4-inch slices to get 7 cups. Put the apples in a bowl and sprinkle with the sugar, flour, cinnamon, nutmeg, and salt. Toss gently and layer the apples into the pie shell, tucking in any apples to create an even, smooth dome. Dot the apples with large flecks of the butter.
Starting at the rim of the pan, stick the dough leaves on the crust and apples, using a little water on the bottom of the leaves to help them adhere. You needn't press the leaves together; they'll seal during baking. Continue to overlap the leaves in concentric circles as shown in the photo below.
Casually overlap the leaves in concentric circles toward the middle of the pie, minimizing the overlapping areas.
Chill the pie in the refrigerator for 15 min. Meanwhile, position two racks to the lower third of the oven, set a foil-lined baking sheet on the lowest rack (to catch any drippings from the pie), and heat the oven to 350°F.
Bake the pie on the second-lowest rack until the crust is deep golden all over and the apples are tender when pierced with a long, thin knife blade, 60 to 80 min. Let the pie cool completely before serving so that the juices have a chance to set up and the filling won't be runny. Serve at room temperature or refresh briefly in a 400°F oven to warm the crust.