Good question, reader Megan! The shortbread recipe calls for corn or rice flour because neither one of those contain any gluten. Not only that, their presence works to undermine the development of gluten by interrupting continuous chains of proteins. Hang on, Joe, you always say that developed gluten needs water, there’s no water in this recipe. Ah, but there is. Don’t forget that butter is 17% water, and that’s all those little protein molecules need to noticeably toughen the dough.
This same trick — of adding a grain flour that contains no gluten — is also employed to tenderize many types of cakes and cookies. If you care to try it, swap one tablespoon of corn starch for a tablespoon of wheat flour in every cup of wheat flour you use.