If you are looking for pure, traditional fats without modern additives or industrial processing, you have a few excellent options that perform exceptionally well in shortbread and hold up reliably in the freezer.
First, high-quality rendered leaf lard is one of the most traditional baking fats available. Leaf lard comes from the visceral fat around the kidneys and has a very neutral flavor compared to standard lard. Because lard forms large fat crystals, it yields a remarkably tender, crumbly shortbread with a crisp snap. It freezes exceptionally well because pure fat contains virtually no water, meaning ice crystals will not form to damage the dough structure during freezing.
Second, ghee, or traditionally clarified butter, is another fantastic option. Ghee is simply pure milk fat with all water and milk solids simmered off. It delivers a rich, slightly nutty and caramelized dairy flavor while behaving like a solid fat. Like lard, ghee is 100 percent fat and freezes flawlessly without losing its texture.
Third, beef tallow, particularly finely rendered suet, can also be used if you do not mind a very subtle savory undertone, though leaf lard and ghee are generally preferred for sweet bakes.
When substituting these fats for standard butter, keep in mind that commercial butter is roughly 80 to 82 percent fat and 16 to 18 percent water. Since pure rendered lard and ghee are 100 percent fat, you should use about 15 to 20 percent less fat by weight, or you can add a tiny splash of milk, cream, or ice water (around one tablespoon per cup of fat) to balance the moisture level. This will ensure your dough binds properly before chilling and freezing.