The most common and most likely answer to this crossword clue is the 4 letter word FILO
F
I
L
O
More clues leading to the result FILO
Buddy explains!

The straight part
We know that "Mediterranean dough" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case mediterranean dough = filo.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 FILO mean?
FILO noun- A type of dough, originating in Mediterranean cuisine, that is used in thin layers to make pastries (such as baklava and apple strudel) and pies and becomes very flaky when cooked.