Pulse the flour, shortening, sugar, vinegar and salt in a food processor until it looks like fine meal. Add the butter and pulse until it is in pea-size pieces. Sprinkle in 1/4 cup ice water and pulse until the dough begins to come together. Pinch the dough with your fingers; if it doesn't hold together, add up to 4 more tablespoons ice water, 1 tablespoon at a time, and pulse again.

Divide the dough between 2 sheets of plastic wrap and pat each into a disk. Wrap tightly and refrigerate until firm, at least 1 hour or preferably overnight, or freeze up to 2 months.