In a food processor, pulse flour and salt. Add butter; pulse until broken up into pieces no larger than peas. Add shortening; pulse until mixture resembles coarse cornmeal, with some pieces of butter still visible.
Sprinkle 1/3 cup ice water on top and pulse until dough just comes together, adding more water if necessary, 1 Tbsp. at a time.
Turn out dough onto a lightly floured surface and knead gently to bring together. Divide dough in half and shape each piece into a disk. Wrap in plastic and chill for at least 1 hour and up to 2 days.
Did not indicate to use both oil and butter or one or the other