Add flour and salt to a bowl, whisk together. Add the butter, tossing to separate the pieces and coat them with flour. Working by hand, pinch the pieces of butter into the flour, forming a good amount of larger flat pieces the size of a nickel or so as well as smaller bits.
Mix egg and milk together. Measure 1/3 a cup of the ice water and a tablespoon of vinegar and add to egg mixture and very quickly (you don’t want to coddle the milk with the vinegar) drizzle the egg/milk/vinegar/water mixture over the flour while tossing with a fork until mostly incorporated.
Turn out on a counter and rub across the mixture two or three times with the heel of your hand, smooshing it as you go. By now, the pastry should be mostly coming together with a few dry areas. Work on those areas by pinching and pushing them into the dough. If necessary add a few sprinkles of water to moisten. The dough should “feel” fairly dry and there may be a few bits that aren’t well incorporated. You should see chunks of butter, through-out.
Gather the dough together into a pile, gently flatten into a squarish shape, wrap in parchment paper or plastic and refrigerate for 1 hour. Overnight is fine, too, and wrapped tightly, the dough can be refrigerated for a day or two or frozen for 1 month. If refrigerated more than an hour, leave the dough at room temperature for 5 to 20 minutes before rolling out.
On a floured work surface, roll out the dough, from the center to edges, 1/8″ thick. Cut into five-inch rounds. You’ll need to reroll the scraps, but to keep them tender, layer them on top of one another, cover with a clean damp cloth and let the rest a few minutes. You can fill the others as you wait. Then just roll the scraps out; the dough should stick together just fine.
Cover the rolled out rounds with a damp cloth as you fill the Empanadas.
For filling and baking, please see my Chipotle Pulled Pork Empanada post.