Without thinking, unfortunately, I poured from that cup less than a tablespoonful of cooled leftover coffee that had milk in it into a fleishig sink where nothing was in the sink at the time. What is the halacha? How is it kashered if that is necessary?
Nothing needs to be done. Rinse the sink, and everything is fine.
Since the coffee was cooled, it cannot impart taste to other utensils and surfaces.