JimLane wrote:

Hmmm, if the butter was deep enough, perhaps it would have fried
the sides in place instead of letting the cheese just run because
too little butter was used?

As a follow-up, did you flour and egg batter the cheese? That
also helps. My recipe calls for frying in olive oil.

***********
Thanks for commenting Jim. The recipe called for just tossing
the cheese in the butter and cooking it without battering. I'm
fairly certain that the way they serve it at our favorite Greek
restaurant, the Trojan Horse in Bloomington, is also unbattered.

Your comment about more butter supporting the sides and keeping
it from spreading is interesting. I was actually thinking of
using very little butter, possibly just buttering the cheese
itself and dropping it in a very hot skillet for mere seconds
per side. We've got more Feta. I'll try another experiment
here soon.

Thanks again, Michael