This buttery, flaky dough is easy to fill and shape to make savory or sweet empanadas.
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Place flour, sugar, and salt in food processor. Lock lid into place. Turn on processor and process mixture for 3 seconds. Stop processor.
Remove lid and sprinkle chilled butter pieces over flour mixture. Lock lid back into place. Hold down pulse button for 1 second, then release. Repeat until mixture looks like coarse crumbs, eight to ten 1-second pulses.
Remove lid and add egg and water. Lock lid back into place. Turn on processor and process until dough comes together into smooth ball, 30 to 45 seconds. Stop processor.
Remove lid and carefully remove processor blade (ask an adult for help). Transfer dough to clean counter.
Use bench scraper or butter knife to cut dough in half. Form each dough piece into 4-inch disk. Wrap each disk in plastic wrap and refrigerate for at least 30 minutes and up to 24 hours. (This is a good time to make your filling! See Empanadas de Piña y Coco.)
Sprinkle flour over clean counter. Unwrap 1 disk of dough, place on floured counter, and sprinkle dough with a little extra flour. Use rolling pin to roll dough into 14-inch circle (about ¼ inch thick), rotating dough and reflouring counter as needed if dough begins to stick.
After placing 1 disk of dough on counter and sprinkling with flour, use rolling pin to roll out dough from center.
Turn dough a quarter turn and roll out from center again. Repeat rotating and rolling dough, reflouring counter in between rolls, until dough forms 14-inch circle.