I love and revere olive oil. I cannot countenance any pasta dish (except carbonara) without olive oil and it must have the finest Tuscan olive oil sprinkled thereon before consumption. No pizza is proper without olive oil, the finest available. I will do that very un-Italian thing of dipping bread in a mix of the best olive oil mixed with the most expensive balsamic vinegar that money can buy. But olive oil has no business anywhere near an omelette. An omelette done that way is no omelette. I once had one of those in an hotel in Italy. That hotel did not understand omelettes. Butter.