The most common and most likely answer to this crossword clue is the 5 plus 3 letter word OLIVE OIL
I've seen this crossword clue in The Daily Telegraph
O
L
I
V
E
O
I
L
More clues leading to the result OLIVE OIL
- Chef right away on counter dropping fine liquid
- We’re told sailor’s girlfriend may be dressing
- Stay in glasses – the Italian’s dressing
- Loves to be in Italy and left with the essence of Mediterranean cooking
- Inflamed swelling originally overlooked by girl when dressing maybe
- Fat girl said she loved Popeye!
- Nothing, as it happens, goes with Polish dressing
- Loves hosting in the flesh with the Italian part of Mediterranean diet
- Fat old couple eating enjoy life at the Italian
- I love mixed grease used in Mediterranean cooking
Buddy explains!
The straight part
We know that "part of Mediterranean diet" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case part of mediterranean diet = olive oil.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.