The trick seems to be too use several carbon steel pans when necessary. One thing you can do in teflon that you can't do in steel is fry up yer veggies and yer meat in the pan, then crack the eggs in, stick-free.

So, use two pans, one foot the fillings and a fresh one for the eggs, adding the fillings once the eggs hit the oiled pan. Afterwards, neither needs more than a rinse out.