Preheat oven to 400F with rack in the upper middle position.
If making the buttermilk substitute, combine the milk and lemon juice and set aside.
Measure out 2 cups of flour in a large bowl. REMOVE 1 Tablespoon of flour from these two cups. Add the cornstarch, sugar, baking soda, cream of tartar, and salt. Whisk to combine.
Using a fork, cut the butter into the flour in a corner of the bowl until the flour is broken down and it looks like wet sand. The butter should not be in large pieces or strips anymore.
Add the buttermilk (or milk mixture), cheddar cheese, and parsley to the flour and use a fork to combine.
Pour out the dough and lightly knead just until everything is combined. It should not be completely smooth.
Pat the dough down into a disk approximately 1 inch tall and 5 inches wide. Transfer to a parchment or silicone mat lined baking sheet.
Using a serrated bread knife, cut an X in the top of the dough approximately 1/2 to 1 inch deep.
Bake the bread until golden brown and a toothpick inserted in the middle comes out with just a few crumbs, approximately 25 minutes.
Let the bread cool on a cooling rack for 1 hour.
You can easily double all the ingredients for a larger, "regular" loaf. Make the disc in step 7 be 2 inches high and 6 inches wide, and cook for closer to 40 minutes.If you do not have buttermilk, combine 3/4 cup whole milk with 2 teaspoons lemon juice and set aside for 5 minutes.