Place 3 cups of the flour, salt, and sugar in a food processor fitted with a blade attachment and pulse until evenly combined. Cut the shortening into small chunks, add it to the food processor, and pulse until the mixture has the consistency of sand.

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.

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. Wrap the dough in plastic wrap and refrigerate for 1 hour.

Lightly flour a clean, large work surface and a rolling pin. Roll the dough out to about ⅛-inch thick. Using a 4-inch-round pastry-cutting mold, cut circles from the dough. (Alternatively use a knife and trace around a 4-inch plate to form the circles.)

Gather the dough scraps and form into a ball again. Roll out the dough and cut more circles. (If the dough springs back and is difficult to roll out, let it rest before rolling again.) Makes about 16 dough circles.

Line 2 baking sheets with parchment paper. Beat the 2 eggs in a small bowl until broken up.

Take 1 of the cut circles and and place 2 heaping tablespoons of the filling in the center. Brush the edges of the empanada with the beaten egg. Fold the circle in half to form a half moon and seal the edges together with a fork or pinch with your fingers. (Be mindful when sealing to squeeze out any air pockets.) Place on the baking sheet. Repeat with the remaining dough circles, spacing the formed empanadas a few inches apart.

Chill the formed empanadas for 20 minutes before baking. Meanwhile, arrange 2 racks to divide the oven into thirds and heat to 375°F.

Place both sheets in the oven and bake for 10 minutes. Rotate the sheets front to back and top to bottom, and continue baking until the empanadas are golden-brown, about 10 minutes more. Let cool a few minutes before serving.