Pre-heat the oven to 425 degrees Fahrenheit. Lightly oil a small cast iron skillet or non stick pan.
In a large mixing bowl, combine the flour, baking soda, cream of tartar, salt, black pepper, rosemary, and chives. Whisk together well. Fold in the cheddar cheese.
In a small mixing bowl, whisk together 1 egg and the buttermilk. Add the milk to the flour and combine well. Dough will be slightly sticky.
Roll the dough into a ball on a lightly floured surface allowing the flour to cover the dough ball.
Place the dough ball on the prepared cast iron skillet (or non-stick pan). Using a knife, slice a large X in the dough. Whisk together the second egg. Using a cooking brush, brush the whisked egg all over the dough ball and sprinkle a dash of salt on top.
Bake for 25 minutes, top should be golden brown when done. Allow to cool for ~10 minutes before slicing and enjoying.