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?
Answer:
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.
Best wishes.