Combine several ice cubes with water in a measuring cup and set aside.
In a food processor, blend flour, sugar, and salt with a few pulses. Add the cold butter and shortening, cut into small cubes, and pulse until the mixture resembles coarse crumbs with some pea-sized bits.
Gradually drizzle in about ⅓ cup of the prepared ice water while pulsing. Scrape down the sides of the bowl to ensure all flour is incorporated. Test the dough by squeezing a handful—if it holds together, it’s ready. If it remains crumbly, add more water a teaspoon at a time.
Transfer the dough onto a lightly floured surface. Gently gather it into a smooth ball without overworking it, then wrap it in plastic wrap and refrigerate for at least an hour (up to 3 days) or freeze for up to a month.