There's only way to cook eggs and that's in a non-stic pan. When you hear grill in relation to eggs it's when the "grill" is a griddle or large flat cooking surface.
A grill pan has nothing to do with grilling. It's an invention not a method of cooking based on technique.
Only similarity between grilling and grill pan is the way the finished product looks.
The point of grilling is yes there is very little fat (though I like to dress items for grilling with extra virgin, chilis, grated garlic , herbs and corriander seed) and that it picks up that great woody smoky flavor from the juices burning on the coals (the big hype now is that this will cause cancer).
Frying is done in a pan. I like to use a heavy guage stainless pan. Non stic is fine but there will not be the sticky bits left in the pan that get reconstituted into the sauce when you deglaze. Although the finished product from non stic saute is a bit more aesthetically pleasing because those drippings and spices stick to the item being seared. You really need to use plenty of oil.
Too little oil will give you a nasty dry fry. The item can be set on cardboard or paper to absorb the oil and will certainy the excess oil from the pan will be discarded. Check out the pan sear and deglaze videos atif
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