In this instance I think it may be ok cooking with the extra virgin. It's such a short amount of time that the oil is really on the heat that there should be very little flavor loss. And what you really want here is the flavor of the extra virgin to be absorbed by the egg as you poach it in oil. Butter would also be very tasty.
Same with the teflon. Most egg pans that you use for eggs are non-stick, though it is possible (though very difficult) to cook eggs in a normal stainless steel pan. The pan is actually on the heat for such a short period of time, that I doubt there will be much teflon fumes.
Just my thoughts.
Harlan
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