Cut the butter in 1/2 inch dice and return it to the refrigerator while you prepare the flour mixture. Place the flour, sugar and salt 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 onto 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 at least 1 inch larger than the pie pan, rolling from the center to the edge, turning and flouring the dough so it doesn't stick to the board. (You should see bits of butter in the dough.) Fold the dough in half, ease it into the pie pan without stretching at all and unfold to fit the pan. With a small sharp paring knife, cut the dough 1 inch larger around than the pan. Fold the edge under and crimp the edge with either your fingers or the tines of a fork.