Beat the butter and cream cheese together using a stand or electric hand mixer. Add the powdered sugar, alternating with the half-and-half or heavy cream. You may not need all of the powdered sugar.
Beat in the vanilla and other extracts, if using. Tint the frosting using natural food coloring drops or powder, if desired. Refrigerate the frosting, covered, until ready to use.
Before decorating the cookies, allow frosting to come to room temperature and stir vigorously to restore the fluffy texture. Frosting can be spread or piped onto cookies.