So my Jewish friends could technically eat a cheese burger, as long as the cheese was placed on the burger after cooking?
Would they have to wait till the burger cools down so that it doesn't melt the cheese? (Here I am concerned about carryover heating/cooking being considered cooking by law.)
I am endlessly fascinated by religious laws and their implications/consequences.
> So my Jewish friends could technically eat a cheese burger, as long as the cheese was placed on the burger after cooking?
No they can't, but this would be a violation of a rabbinical law (the rabbis forbade eating them together as a safeguard), which is less serious than a biblical law violation.
> Would they have to wait till the burger cools down so that it doesn't melt the cheese? (Here I am concerned about carryover heating/cooking being considered cooking by law.)
The real question you are asking is what counts as cooking. This has lots of ramifications in Jewish law, particularly because cooking in general is forbidden on the sabbath. From here, you can go down the rabbit hole of related questions. What temperature counts as cooking? If something has a low melting point, is it treated differently or is there an absolute temperature? Can you keep things warm on the Sabbath if they are already cooked? Can you rewarm them? I can go on and on, but the gist is that it gets complicated and this is the reason why there are many people who spend a lifetime learning talmud and never master it.
But to answer your question specifically, waiting for the burger to cool down is irrelevant in this case since it's rabbinically prohibited to eat them together anyway. The only real question is at what temperature it goes from a rabbinical to a biblical prohibition.
You would have to find someone who counted the validity of the original law ("Thou shalt not seethe a kid in its mother's milk" in Exodus https://www.mechon-mamre.org/p/pt/pt0223.htm) but did not count any later interpretation or fence around it.
Please talk to your participants well before you start this experiment; very few people are going to have an equivocal attitude towards it.
Would they have to wait till the burger cools down so that it doesn't melt the cheese? (Here I am concerned about carryover heating/cooking being considered cooking by law.)
I am endlessly fascinated by religious laws and their implications/consequences.