1. Place 3 cups of the flour, salt, and sugar in a food processor fitted with a blade attachment and pulse until evenly combined.
2. Cut the shortening into small chunks, add it to the food processor, and pulse until the mixture has the consistency of sand.
3. Whisk the egg, water, and vinegar in a small bowl until combined. Turn on the food processor and slowly pour in the egg mixture. Continue mixing until the mixture resembles coarse crumbs.
5. Empty mixture onto a lightly floured work surface and use your hands to shape it into a rough ball. Using the heels of your hands, gently knead the dough into a smooth, elastic ball.
7. Wrap the dough in plastic wrap and refrigerate for 1 hour.