In a large bowl, combine flour and salt. Cut in the cold butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs.
In a separate bowl, whisk together the egg, warm water, milk, and sugar.
Gradually add the wet ingredients to the dry ingredients, mixing until a dough forms. Knead briefly until smooth. Wrap the dough in plastic wrap and let it rest in the refrigerator for at least 30 minutes.
In a medium bowl, mix together the cheese, chopped onions, ham or bacon, and parsley or cilantro (if using). Season with salt and pepper to taste.
On a lightly floured surface, roll out the dough to about 1/8 inch thickness. Cut out circles using a cookie cutter or the rim of a glass (about 4-5 inches in diameter).
Place a spoonful of the filling in the center of each dough circle.
Fold the dough over to form a half-moon shape and press the edges together to seal. Use a fork to crimp the edges if desired.
Heat vegetable oil in a deep skillet or fryer to 350°F (175°C).
Fry the empanadas in batches until golden brown and crispy, about 2-3 minutes per side. Remove with a slotted spoon and drain on paper towels.
Enjoy your meal!