"A variety of X is" vs. "a variety of X are"

Which of the following sentences is correct?

• A variety of dishes are being prepared.
• A variety of dishes is being prepared.

I believe that both can be used, though I'd stick with the plural use of the verb. What do you think?

Both sentences are grammatical. The first makes us aware of the individual items in the variety. The second foregrounds the variety itself.

Here are the actual usage stats from the British National Corpus (BNC) and the Corpus of Contemporary American English (COCA):

                                BNC      COCA

a variety of [n*]/[nn2] is     15/11     47/15
a variety of [n*]/[nn2] are    26/26     83/82

ratio plural:singular         1.7/2.4   1.8/5.5

For those unfamiliar with the query syntax, [n*] stands for any noun form, while [nn2] stands specifically for "plural common noun".

An important thing to note is that this has nothing to do with the verb immediately following the plural noun. We can move the verb directly in front of "a variety", but the preference for plural agreement doesn't change:

                                         BNC           COCA

there is a variety of /[n*]/[nn2]     23/16/12      17/  9/  6
there are a variety of /[n*]/[nn2]    56/37/34     260/187/172

ratio plural:singular               2.4/2.3/2.8  15.3/20.8/28.7

In short, plural is the agreement of choice on both sides of the pond, though interestingly considerably more so in the US.

And as you pointed out yourself in comments elsewhere on this page, this is not really surprising, but in fact perfectly in line with how similar constructions such as a number, a lot, a total, etc. behave. This is sometimes referred to as notional agreement or notional concord:

As Quirk et al. 1985 explains it, notional agreement (called notional concord by Quirk and others) is agreement of a verb with its subject or of a pronoun with its antedecent in accordance with the notion of number rather than with the presence of an overt grammatical marker for that notion. Another way to look at the matter is that of Roberts 1954, who explains that notional agreement is agreement based on meaning rather than form.

In Wikipedia, the corresponding entry is to be found under synesis:

Synesis [...] is effectively an agreement of words with the sense, instead of the morphosyntactic form. [...] Such use in English grammar is often called notional agreement (or notional concord), because the agreement is with the notion of what the noun means, rather than the strict grammatical form of the noun (the normative formal agreement). The term situational agreement is also found[.]

Notional agreement for collective nouns is very common in British English. It is less customary in American English, but may sometimes be found after phrases of the type "a collective noun of plural nouns", e.g.,

• ... a multitude of elements were intertwined. (New York Review of Books)
• ... the majority of all the shareholdings are in the hands of women. (Daedalus)
• ... a handful of bathers were bobbing about in the waves. (Philip Roth)

I would say that for "a variety of dishes", the verb should agree with either "variety" or "dishes", depending on which is the actual noun the verb acts on. There are a variety of phrases "a [noun] of" for which this is the rule (although for most phrases "a [noun] of", the verb must agree with [noun]).

Here is a variety of examples, the first two of which sound wrong (and alter the meaning) if you change the verb.

A wide variety of dishes is essential for a successful restaurant.

The dishes individually aren't essential; it's having the wide variety of them that is.

A variety of side dishes make a good accompaniment to fish.

You don't serve the fish with the variety, just with one of them.

A variety of dishes is/are being prepared.

Both the individual dishes and the whole variety of them are being prepared, so either verb works.

The case of "a number of" is clear, logical and natural: "A number of customers has complained about this" just sounds weird, while "The number of complaining customers has increased" sounds fine. If we apply the same logic to "variety of" (and why shouldn't we?), these sentences sound fine: "The variety of such systems has quickly expanded." Or, "A variety of such systems are equipped with lasers."