MMario, I think you're right. gnu's description reminded me of a time when a bunch of eggs were fried up in a pan just after the bacon, when all the grease had been left in the pan.

So if the fat is hot, but not in contact with the egg & there has been no contact with water either, what kind of egg is it? Coddled?

I do like the taste of eggs fried in the pan that's just been used for sausage or bacon, but normally I drain off most of the grease. All those meat bits left behind really enhance the taste.