In a glass measuring cup, combine vinegar and milk and set aside for at least 5 minutes.
In your stand mixer bowl, combine all the dry ingredients including the sugar. Then cut in the butter. Rub it in with your fingers until the mixture looks grainy.
Beat the egg into the milk mixture.
Attach your dough hook to your mixer. While the mixer runs at the lowest speed, slowly drizzle in the liquid. Do this quickly after beating in the egg.
Once combined, switch to a dough hook and run on low-medium speed for 5 minutes.
Turn the dough out onto a floured counter, and divide into 2. Roll each into a ball with a tight skin.
Coat 2 round cake pans in oil, and place the dough in the center, lightly pressing it down but not all the way to the edges.
Using a sharp knife, cut an X across the tops.
Dust with turbinado sugar if you want.
Bake for 30 to 40 minutes if using a dark non-stick. It will take longer if you use lighter-colored metal or glass pie plates.
Cool in the pan for 5 minutes, then remove to a cooling rack to continue cooking to room temperature.
Serve alongside your favorite Saint Patrick's Day meals!