For the longest time I struggled with cleaning up after pans that we'd cooked eggs in. It seemed that no amount of scrubbing or soaking would help. In search of answers, I googled.
The answer lies in water temperature. Clean those scrambled egg pans and poached egg cups in cold water first. Using hot water only serves to cook the egg more and affix it to the pan. Once it's clean, follow up with soap and a hot rinse.
Also helpful, coat your cooking pans with the magical lecithin mixture. You'll be amazed at how easy clean-up becomes!