Sift the flour, sugar, and salt into a large bowl. Using your fingers, work in the butter and shortening until the mixture resembles coarse crumbs. Add 2 tablespoons of ice water and work with your fingers until the water is incorporated and the dough comes together. Add more water as needed to make a smooth dough, being careful not to over-mix. Form the dough into a disk, wrap tightly in plastic wrap, and refrigerate for at least 30 minutes before using.