Roll larger dough disc out to 14 to 16 inches in diameter and transfer the dough to a 9-inch deep dish pie plate, letting it slump into the dish. Gently tuck into the dish and trim edges leaving about 1/2-inch overhang. Chill while rolling out top crust.
Roll out remaining disc to about 12 to 14 inches in diameter. For a lattice, cut into 12 one-inch strips. To alternate with braids, divide the disc in half and cut one half into the one-inch strips (I cut 5 strips). Cut the other half into thin strips of 1/2 centimeter width (I cut 9 to braid into 3 braids). To braid, gather 3 thin strands and pinch at the top and braid together, pinching the dough together again at the end. Transfer all the strips to a parchment-lined baking sheet and chill for 10 to 15 minutes.
Preheat the oven to 425°F.
Spoon the filling into the bottom pie shell.
Place the top crust over the apples and bring the overhanging bottom crust up and over the top crust, pinching to seal and then crimping. If making a lattice, tuck the strips under the bottom crust edge and then crimp. Cut decorative vent holes if using whole top crust. Brush crust with egg wash and sprinkle with coarse sugar. Chill whole pie for 10 to 15 minutes.
Place the pie on a parchment-lined baking sheet. Bake the pie for 20 minutes, then reduce the oven temperature to 375°F and bake for 40 to 55 minutes more, until you see the filling bubbling inside the pie. Check the pie after 30 minutes and cover the edges with foil if browning too quickly.
When done, remove pie from oven and let cool. For best results, let pie set for at least 3 hours or overnight.
Store pie lightly covered at room temperature for a few days.