I don’t know if I’ve ever had that happened, and I pretty much exclusively order over easy.
I wasn’t trying to name a precise dish. But there are several ways to cook eggs. Fried, boiled, and poached being the most common. All of those come on different degrees of doneness.
I’ve mostly taken to boiling eggs if I’m just cooking for me, rather than frying them, because there’s less to clean up. I want runny yolks either way.
I only do hard boiled eggs for passover or when I’m cooking for other people.
The trick I use with my beautiful non-stick T-Fal fry pan requires pretty much no cleanup and is consistent not only with low effort, but I’m sure has been responsible for preserving the perfect like-new non-stick quality for at least a decade and a half.
I fry eggs in butter in the sunny side up style as I mentioned, but covered with foil to start cooking the yolks just a little. They slide onto a plate in perfect formation with just a nudge from a spatula, Then I usually throw on a few slices of pre-cooked bacon for just a few seconds – it’s an expensive way to buy bacon but well worth the convenience.
Then, while the fry pan is still warm, I just wipe it down with paper towel until it’s gleaming – there’s usually nothing in it anyway except a bit of melted butter and maybe a dab of bacon fat.
I have another non-stick fry pan with a glass cover that I use for heavier duty stuff that can sometimes get grungy, and that one I will, if necessary, wash gently in soap and water. Neither of them ever go in the dishwasher (the cover does, though), and the magnificent T-Fal has never encountered even mild dishwashing soap.
Perhaps for bad reasons, i don’t use no-stick pans. I even replaced my husband’s pancake pan with one that’s coated in carbon steel recently. (He tested it and declared it fine before i actually got rid of the old one.)
I think non-stick fry pans have gotten an undeserved bad rap for a couple of reasons. One was that early Teflon manufacturing processes involved the use of perfluorooctanoic acid (PFOA). It had multiple toxic effects on workers exposed to it in the manufacture of Teflon, including increased cancer risk, resulting in major news stories, scandals, and lawsuits. However, the actual Teflon product itself didn’t contain PFOA, and in any case the use of PFOA was banned over a decade ago, at least in first-world countries.
The other risk which remains true today is that severely overheating non-stick cookware releases fumes that are potentially toxic (at least to canaries!). The trick there is – don’t severely overheat it!
We should each use what we’re comfortable with. None of my saucepans are non-stick. I have a beautiful heavy Kitchenaid stainless steel saucepan with a layer of copper cladding between the steel layers that I use all the time, and a heavy Cuisinart fry pan that I use for sauteeing. But I swear by my T-Fal non-stick for eggs and bacon!
If I heard “boiled eggs”, I would assume, absent any other context, that hard-boiled was meant. But I’d always add the “hard-”, myself.
Like far too many to pleasantly @, I would expect an “over medium” egg to have a yolk that was close to a partially solidified gelatin or summer room temperature butter (75-80F, very soft but not melted). Not runny, not a solid mass, but in, duh, the middle.
I agree with the dislike of runny whites, but I find the fully cooked yolks more disturbing than possibly underdone whites. Which is why if I’m getting breakfast or breakfast-for-dinner out, I’m not looking for eggs. Maybe an omelet, but generally I want something that’s too much work / bother / prep to do at home, like good French Toast or Waffles.
Over easy eggs are best to make and have at home, for no other reason than the cost of a restaurant prepared egg breakfast compared to ingredient cost!
When I’m making over easy eggs at home, I’m also generally eying a breakfast sandwich element. Two eggs, three slices of toast. Half the eggs, leaving a lovely golden pool of yolk. Each of the first two pieces of toast (sourdough ideally) get a drained egg with plenty of clinging yolk, with heavy pepper and light salt, eaten open faced sandwich style. The last piece of toast gets to sop up all the remaining yolk with a bit of extra pepper and salt again.
Eggs over medium work for this, though not as well, needing more spreading and less sopping.
If I was looking for that sort of half-solid gooeiness I’d just order a poached egg. Over medium is just too small a target for a harried breakfast chef.
Regarding undercooked runny egg whites how are those making it out the kitchen door to be served to customers. Does any one order eggs like that and I’m pretty sure that would be considered a health risk they’d like to avoid.
When I worked as a fry cook, over medium was the breakfast equivalent of ordering a 2" ribeye well done.
Perhaps, but this thread is making be appreciate how uncomplicated my life is as one who orders (and enjoys) my eggs “up.” I know some (many?) folks are uncomfortable with the snot-like texture of lightly cooked eggs, but lucky me, I’m quite delighted with it.
I also like okra.
And hominy grits? 
My you are twisted. Do you have a hairless cat to stroke? 
My steak rare my eggs medium.
I used to order my eggs sunny side up.
I’ve switched to over medium.
I want the egg white cooked. Yolk should be almost cooked. Just a little runny in the middle.
It’s not hard to achieve. Flip the egg. Let the yolk kiss the hot pan for about 10 seconds.
I haven’t discovered the gelatinous joys of eggs up
Im not sure I can allow the eggs to do their thing without fuss.
Slight hijack, but I’m going to mention something I noticed a couple of months ago. In February, we spent 12 days in New Zealand. We went out for breakfast most of those days. Without fail, each and every restaurant had three ways to order eggs: fried, scrambled, and poached. I ordered them fried just once, and received them sunny side up. After that, I ordered scrambled, unless I ordered Eggs Benedict, which was available on almost every menu.
Carry on.
Yes, this.
It’s only in the states that I’ve seen such a wide variety of egg orders. Most places it’s as you say: scramble, fried, or poached.
Even in the US, some folks will order their eggs just “fried”, which seems to encompass everything from sunny-side to over-hard.