This is Grandma Martone's recipe, and a really great sugar cookie: very flavorful, even when made without the walnuts. I always make two double batches; one with nuts and one without because of folks' individual preferences. I put red sugar on the no-nuts ones and green sugar on the nut ones ("green means go"... nuts!). I've made them before by just rolling balls of dough and pressing them flat, but they're not the same: softer, not as crisp. If you chill the dough in logs and slice it, as mom has done on occasion, you can get that crisp texture without having to roll them out and using cookie cutters.
These don't have to just be for Christmas. One year they were class valentines!