Cooking can be a great leveller. Not only do you get a lovely meal at the end of the process which in itself presents the opportunity for casual and friendly discussion but the process itself puts people on a level playing field. Muddleing through a recipe that you've never made, with people, gives you all a chance to get things wrong, have small triumphs and get to know each other.
We all need to eat and so food is a great way to provide a visual metaphor that reminds everyone that we are all humans not a set of characters- "Teacher", "Parent"and "learner.
I'm not sure how the logistics would work here, but perhaps others do.