What is the plural for "Egg in a hole"?

Any one of these is arguably fine:

eggs in a hole
eggs in holes
egg-in-a-holes,

where the last one must include the hyphens.

Egg in a hole is the name of a dish. Typically, this is a fried egg that is dropped into a hole that was cut into a piece of toast. For a typical recipe, see here. That website says that toad in a hole is an alternative name. There is also toad in the hole, which apparently has a sausage instead of an egg (see here).

Discussion

First, let's see how pig in a blanket is pluralized. (Pig in a blanket is a popular finger food, typically a hot dog served in a wrapper of baked dough. For a typical recipe, see here.)

Pig in a blanket: dictionaries

According to both the OED and Merriam-Webster, either pigs in a blanket or pigs in blankets is fine. Oxford Dictionaries has it as pigs in a blanket; Collins and Macmillan as pigs in blankets.

Pig in a blanket: google books Ngram

While there are some false positives where pigs in a blanket is used in its literal meaning (e.g. here), looking through google books, it seems that an overwhelming majority of hits for it (and there are many) does correspond to the name of the dish. Furthermore, for pigs in blankets I was unable to find it used in any other context except as the name of the dish. Thus an Ngram comparing these two is probably reliable, and it says that pigs in a blanket is about twice as common as pigs in blankets (see here).

Unfortunately, the Ngram viewer refuses to search for pig-in-a-blankets and finds no hits for pig in a blankets.

Pig in a blanket: google books

Currently there are three occurences of pig-in-a-blankets: here, here, and here.

Pig in a blanket: Conclusion

Both pigs in a blanket or pigs in blankets is fine, though the former is about twice more common. A few sources use pig-in-a-blankets (always hyphenated), but this is quite rare in comparison with the other two.

Egg in a hole: dictionaries

Unfortunately, it seems that no dictionary has an entry for egg in a hole at the present time.

Egg in a hole: google books Ngram

Looking through google books for eggs in a hole and eggs in holes, it seems that an overwhelming majority of hits use the literal meaning of these phrases, like

The female turtle lays eggs in a hole she digs on a particular nesting beach. (source)
Mr. Todd did you ever try packing eggs in holes bored through boards and then laced in barrels and then turn them occasionally until the time they are sold? (source)

Thus the Ngram is not really useful in this case: one really needs to look at the context of how a search-string match appears in the source. In addition, just like we saw above for pig-in-a-blankets/pig in a blankets, the Ngram viewer refuses to search for egg-in-a-holes (here) and finds no hits for egg in a holes (here).

Egg in a hole: google books

First of all, there were three hits for egg-in-a-holes, always hyphenated: here, here, and here.

In order to try to filter out the irrelevant hits for the other two possibilities, we can try adding recipe to the search.

There is one hit for "eggs in a hole" recipe:

With a few children assisting at a time, prepare "Eggs in a Hole." (source)

There is also

Extra-coconutty eggs-in-a-hole (source),

but this is probably a different dish than the one you have in mind.

A search for "eggs in holes" recipe returned no relevant hits.

Egg in a hole: the internet at large

Because of the low rate of hits on google books, we may consider the desperate step of trying to glean how popular the various versions are on the web in general. For what it's worth, having superficially scanned the results of searches for '"eggs in a hole" recipe', '"eggs in holes" recipe', and '"egg-in-a-holes" recipe', it seems to me that 1. all three are represented, and 2. eggs in a hole is the most popular, followed by eggs in holes.

Conclusion

An analogy with how pig in a blanket is pluralized would suggest that eggs in a hole and eggs in holes are both fine, while egg-in-a-holes is only marginally so. However, so far there seem to be comparably more hits in published literature for egg-in-a-holes than for either of the other two. The overall hit rate is very small, on the order of 1-3 hits, so the statistics are not very strong. Perhaps from this we can tentatively conclude that, relative to their respective alternatives, egg-in-a-holes is more acceptable that pig-in-a-blankets. Finally, the results of a search of the internet at large seem to be consistent with the claim that all three are acceptable, with eggs in a hole being the most popular, followed by eggs in holes.

It's about what you want to convey.

Eggs in a hole

indicates there is more than one egg, and they're all in one hole.

Egg in a holes

doesn't work at all, because you have an article and noun disagreement.

Egg in holes

indicates there's one egg, and it's in a bunch of different holes. Either the egg has somehow learned how to be multiple places at once, or, more likely, it's in a bunch of different pieces.

Eggs in holes

says there's a bunch of eggs, and they're in a bunch of different holes. It's unclear if there are more eggs than holes, or more holes than eggs, or if it's a one to one relationship. It could be that some holes have multiple eggs, while others have bits of an egg spread between them.

Edit: while ordering off of a menu, I'd probably go with

Two orders of eggs in holes.

One would presume that

• multiple instances of a dish called 'an egg in a hole' would each come with their own hole
• the wait staff doesn't care about your word usage, but maximizing the plurality won't go wrong.

I’d order two egg-in-a-holes.

It seems, to me, unpretentious and clear, especially if you treat egg-in-a-hole as a monolithic thing.

EDIT: An earlier version of this answer used some examples were not exactly right so they’re now deleted. Just mentioning this so that the comments below make sense.