Dice the butter and return it to the refrigerator while you prepare the flour mixture. Place the flour, salt, and sugar in the bowl of a food processor fitted with a steel blade and pulse a few times to mix. Add the butter and shortening. Pulse 8 to 12 times, until the butter is the size of peas. With the machine running, pour the ice water down the feed tube and pulse the machine until the dough begins to form a ball. Dump out on a floured board and roll into a ball. Wrap in plastic wrap and refrigerate for 30 minutes.
Cut the dough in half. Roll each piece on a well-floured board into a circle, rolling from the center to the edge, turning and flouring the dough to make sure it doesn't stick to the board. Fold the dough in half, place in a pie pan, and unfold to fit the pan. Repeat with the top crust.