As a Brazilian, I love tapioca, not that drink, but tapioca origin of the word. It is a dish made of melted cassava starch, stuffed with meat, cheese, ham, smoked turkey breast, etc.
By the guy's description, he just has to down the cup as fast as possible. Or possibly just vomit into the cup and look like a weirdo. Oh, and stop them from serving anyone else, I guess.
What bothers me with the bare facts of the premise provided instead is: How were they storing this 'tapioca' in the first place? In a giant milk vat? If so, how'd they run out of milk? If not, how'd they get through the conversation just now without everyone dying?
Obviously this is taking the absurdist premise way too seriously and all.