In the bowl of a food processor, combine the flour, sugar, and salt. Pulse to combine. Add the butter and shortening, and pulse until the mixture forms little balls, and no chunks of butter or shortening remain, 5 to 10 times. Do not over process.
Transfer to a large bowl. Sprinkle with 1 tablespoon of the ice water. Repeat 3 times more. Using your hands or a wooden spoon, stir the mixture until it just begins to come together as a dough. If necessary, add more water, 1 tablespoon at a time.
Divide the dough into 2 disks. Wrap in plastic wrap, and refrigerate for at least 30 minutes.