First I didn’t understand what RebYidd’s post had to do with this thread: it has nothing to do with the recipe, but questions the whole premise of black-and-whites altogether. Next I wondered what his question was supposed to mean. Why “this particular type of cookie”? Because it’s a black and white. By definition it’s two colors–that’s what makes it a black and white, and that’s why it always has two colors.
Then, I realized that kushya mituretzes b’chaverta–if the OP wanted a recipe for black and white cookies, and not black and white frosting, then there is obviously only a certain cookie which could be made into black and whites.