What's an accurate easy-to-understand way of referring to the brown outer part of a fried egg?
the crispy part? (of food, typically cooked food) having a pleasingly firm, dry, and brittle surface or texture; pleasantly thin, dry, and easily broken, appealingly crunchy
I would use the crisp of an egg. (having close stiff or wiry curls or waves)
"crispy edges" or "burnt edges" is easy to understand.
Note: These or similar phrases are used in "how to fry an egg" tutorials also. Especially how not to get them when frying.
For example:
https://cooking.stackexchange.com/questions/33501/how-to-fry-an-egg-without-a-burnt-thin-crust-around
http://www.wikihow.com/Fry-an-Egg