To me, "over easy" seems to refer to the pan, because I think of a pan sitting atop an easy flame. "Over hard" makes me think it refers to the egg, because the liquid becomes solid. Then again, maybe it's something else altogether.
4 Answers
There's not really such a thing as over easy scrambled eggs. It originates with fried eggs, where it means turn them over gently (easy, carefully) and cook for for a few seconds more before serving, so the white is fully set (not "snotty"). That's gently because you don't want to break the yolk.
The opposite to over easy is sunny side up (i.e. - don't do that turning over).
EDIT: Because over easy is so well-known in the above context, and because there are no other standard terms to describe how you want your eggs (unlike, say, rare, medium, bloody, well-done for steaks), people do sometimes extrapolate variants such as over hard, or apply over easy to scrambled eggs. They're easily understood, but such usages aren't really standard terminology.
EDIT2: It never occurred to me anyone would propose an alternative origin for over easy. Having scoured the Internet, I don't see anything looking remotely like an "authoritative" etymological reference - so unless someone else does, all I can offer is a couple of links supporting what I think...
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Actually a colleague with a heart transplant needed to order eggs over "hard" because no part of the fried egg could be under cooked - though I'm sure that phrase would be exceedingly rare. Commented Jan 27, 2013 at 23:15
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10I'm pretty sure over medium and over hard are recognized terms: they all mean that the egg should be fried on both sides, but cooked more than over easy. An egg cooked over easy will have a fully cooked white but a runny yolk, when over medium the yolk is mostly congealed, and when over hard the yolk is completely solid. I've ordered eggs both ways in restaurants (in the US) and never been asked to clarify. It's neither exceedingly rare nor facetious, just not as popular among diners. Google has lots of hits for both. Commented Jan 27, 2013 at 23:29
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1For scrambled eggs, you just drop the over. That's how I order mine anyway: "Eggs scrambled hard." I've never had a server ask me what I meant and I usually get them the way I wanted them, so I assume it's standard lingo.– Kit Z. Fox ♦Commented Jan 28, 2013 at 2:54
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1@Mitch: The question is drifting well beyond its original scope, which was to explain the reason why we use the words over easy. I'm saying it's because you turn them over "easy" with a spatula, Kate says it's derived from an earlier "hard" [-cooked yolk], and Kaz says it's from an easy=soft/gentle heat source. Vote on that, and leave the recipes and related specialised terminology to other questions and/or other sites. Commented Jan 28, 2013 at 3:49
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1... this isn't a credible source, but since I believe "in order to faciliate lightly cooking the yolk, you would have to flip the eggs over, and to prevent the yolk from breaking (and rendering the eggs "cooked hard") you have to flip them over easy" is correct, there's the link. Commented Jan 28, 2013 at 14:05
I'm pretty sure that "over hard" came first: it's diner jargon that the eggs should be flipped over and cooked until they are hard. Now if you want it flipped but not hard, well the opposite of hard is easy, right? (Sure, you could say soft or runny, but diner slang is often supposed to be funny, a bit of an in-joke, and opaque.)
Most likely, easy refers to going easy on the temperature and duration, and hard on the condition of the egg, as you suspect. We can play hard and work hard, but we don't really speak about cooking hard. The egg yolk gets solidifies atop even an easy flame, given enough time. And of course, easy doesn't refer to the liquid condition of the yolk.
These terms refer to the egg, namely to its degree of cooked-ness: over-easy is cooked on both sides but yolk is runny; over-medium is less runny than over-easy, and over-hard is when both the yolk and white is cooked all the way through.
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2Welcome to EL&U. Please note that this is not a discussion forum, but a Q&A site, yet your submission does not attempt to answer the question. I encourage you to take the site tour and review the help center for additional guidance.– chosterCommented Oct 1, 2015 at 17:12