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1
Process the flour, sugar, and salt together in a food processor until combined, about 6 seconds. Scatter the butter pieces over the flour mixture and pulse until the mixture resembles coarse crumbs with butter bits no larger than small peas, about 16 pulses.
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2
Transfer the flour mixture to a large mixing bowl. Working with 1/4 cup of water at a time, sprinkle the water over the flour mixture and stir it in using a rubber spatula, pressing the mixture against the side of the bowl to form a dough, until no small bits of flour remain (you may not need to use all of the water).
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3
Turn the dough out onto a clean work surface and divide it into 2 equal pieces. Press each dough half into a cohesive ball, then flatten the ball into a 6-inch disk. Wrap each disk in plastic and refrigerate until firm but not hard, about 2 hours.
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4
While the dough rests, place pulled pork in a small bowl and add enough vinegar sauce until meat is very moist (you may not need the entire 1/2 cup of sauce).
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5
Preheat oven to 425 degrees. Line 2 baking sheets with parchment paper; set aside. Remove 1 disk of dough from the refrigerator. Roll the dough out on a lightly floured work surface into an 18-inch circle about 1/8 inch thick. Using a 3-inch round biscuit cutter, cut out 18 rounds and transfer them to the prepared baking sheet, discarding the dough scraps. Place a heaping tablespoon of pulled pork to the middle of each round. Seal dough around filling, using tines of a fork to crimp edges shut. Repeat with second disk of dough and second prepared baking sheet.
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6
Brush empanadas with the egg. Bake until golden brown, 20 to 25 minutes, switching and rotating the trays halfway through the baking time. Let cool for 5 minutes. Transfer to a platter and serve with a bowl of barbecue sauce, if desired.
