Rudolph Chelminski discusses the cooking of eggs in his book The Perfectionist. Bernard Loiseau believed the egg should not touch the heat of the pan. He cooked the egg on a buttered saucer over a pan of boiling water. He even went as far as separating the white from the egg and putting them together after they were cooked.
Could this make a difference to the taste of the egg? Believe me when I say it does. The method is a little time consuming and obviously not for those in a hurry in the mornings.
I lined an espresso cup and saucer with Gladwrap. The eggs were separated with the white on the saucer which went into the pan first. When the egg white started to turn opaque I then added the the yolk in the cup. I placed a paper towel over the top of the saucepan and partially covered the pan with the saucepan lid. A few minutes later the white had set and the yolk had that cooked look. They were then put back together on the plate. I salted the white first as Mme Saint-Ange says to salt the white only so as not to leave spots on the yolk.
It was good. So good I licked the plate clean!