The most common and most likely answer to this crossword clue is the 8 letter word LASAGNAS
I've seen this crossword clue in Financial Times
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The straight part
We know that "Mediterranean dishes" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case mediterranean dishes = lasagnas.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does LASAGNAS mean?
LASAGNAS noun- A flat sheet of pasta.
- An Italian baked dish comprising layers of such pasta with various ingredients (usually a meat ragù (chiefly Bolognese), a fish ragù or a vegetarian/vegetable ragù with bechamel sauce)