As an example, I made eggs using Gordon Ramsay's Perfect Scrambled Eggs, at the end the pan ends up having a layer of eggs attached to the bottom and sides that is very difficult to wash (not a nonstick pan).  I found some recommendations online, but none of them have worked very well.  Maybe there is no good way?   Baking soda Run under cold water instead of hot  
i know this is an old post, but i believe i've cracked this code, if you put an inch and a half or so of water in the pan and let it sit on medium heat for four or five minutes, rinsing the pan removes most of the egg, swiping with your finger, has the rest come off instantly 