Yes! Follow these steps to store it properly: Once you have made the cookie buttercream, transfer it to an airtight container. Cover the top of the frosting with plastic wrap to prevent it from forming a crust, and seal the container tightly. Label the container with the date and contents, then store it in the refrigerator for up to a week or in the freezer for up to a month. When you are ready to use the frosting, remove it from the refrigerator or freezer and let it come to room temperature. Give it a quick stir or re-whip it in the mixer to make it fluffy again, adding more milk or powdered sugar if needed to get the right consistency. Top tip: If you freeze the frosting, you may need to take a long time to thaw it in the refrigerator before using it. Also, keep in mind that the texture and flavor of the frosting may change slightly after being stored, so it's a good idea to taste and adjust it as needed before using it to frost your cake.