Pulse flour, salt, butter, and shortening in a food processor until mixture resembles coarse meal. With processor running, drizzle in 1/4 cup water until dough just comes together. (If dough is still crumbly, add up to 1/4 cup more ice water, 1 tablespoon at a time.) Do not process for more than 20 seconds. Divide dough in half; wrap each in plastic. Refrigerate until cold, about 30 minutes.