For those of you lucky enough to have not lived in Utica, New York, you may have missed out on a true half-moon cookie. Although I feel like I'm probably perpetuating pro-Utica propaganda, the central New York half-moon isn't usually recreated correctly elsewhere. If you find someone who knows where Rome, New York is, they're probably familiar enough with the area to be able to tell you about the difference between a half-moon and the cookies that are sold around the rest of the country.
A correct half-moon is more cake than cookie on the bottom, and should have a softer icing on the top than many other cookies. That is, it shouldn't be an icing that hardens. Something between a cupcake's icing and the sort of hard icing that is just powdered sugar.
Unfortunately, that's all the icing I knew how to make, so that's what my cookies got. We'll see how it worked in a little while when I finally get to eat them. In the meantime, though, I'm just going to leave this link here. You can go look at it if you want. I'm going to eat a cookie.