To make these Christmas Eggnog Sugar Cookies gluten-free, substitute the all-purpose flour with a 1:1 gluten-free baking flour blend that includes xanthan gum. Ensure all other ingredients, including the baking soda and extracts, are certified gluten-free. The dough may be slightly softer, so chilling it for 10–15 minutes before rolling can help maintain structure. The cookies will retain their buttery flavor and festive eggnog aroma while remaining tender and light.