The speaker is making a repeated reference to revenge.
There's a proverb in English that says:
Revenge is a dish best served cold.
The popular expression "revenge is a dish best served cold" suggests that revenge is more satisfying if enacted when unexpected or long feared, inverting traditional civilized revulsion toward "cold-blooded" violence.
Simplified, it means that it's best to take revenge on someone when they least expect it, and especially when some time has passed from the event that caused the person to seek revenge (i.e., the proverbial dish got cold). The coolness of the dish might also suggest that the person plotting an act of revenge is doing so in a cool and calculated manner.
Although the idea must be as old as people, the origin of the phrase/metaphor isn't known for sure. You can learn more about it by reading the rest of the linked section of that Wikipedia article.
By the way, I wouldn't concern myself with how exactly they phrased it – i.e., who served the dish to whom – you have to take into consideration the fact that this is a scripted show and the writers probably decided that was the best way to deliver the joke.
That said, I believe the intended meaning of the original saying is that the person exacting revenge on the other is the one eating (being served) the dish. However, an extended debate would be of little value as different people understand the proverb differently nowadays.