This Potato Parsley Cakes recipe can be gluten free as written, provided the mashed potatoes and any instant potato products used are certified gluten free. If using instant mashed potatoes, check the packaging carefully to confirm there are no gluten-containing additives or cross-contact warnings. Butter, parsley, salt, and pepper are typically gluten free, but it is still a good idea to verify labels when cooking for someone with celiac disease or gluten sensitivity. No further substitutions are needed if all packaged ingredients are confirmed gluten free.