In the bowl of a food processor, combine flour, sugar, and salt; pulse to combine.
Sprinkle shortening over flour mixture and process until flour resembles course cornmeal, about 5 pulses. Sprinkle butter over flour mixture and pulse until crumbs are slightly smaller than pea-sized, 15–20 pulses.
Transfer dough mixture to a large bowl and sprinkle 3 tablespoons of ice water over dough.
Using a rubber spatula, mix water into dough, pressing the dough together. If the dough doesn’t come together add remaining tablespoon of ice water and mix until dough is cohesive.
Turn dough out onto a clean, flat surface, flatten into a 4-inch disk and wrap with plastic wrap; transfer to refrigerator and chill 1 hour.
Remove dough from refrigerator and let stand at room temperature for 10 minutes before rolling out. Use to make desired pie or galette.