The most common and most likely answer to this crossword clue is the 7 letter word FALAFEL
I've seen this crossword clue in The Guardian
F
A
L
A
F
E
L
More clues leading to the result FALAFEL
Buddy explains!

The straight part
We know that "Middle East food/Middle East food" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case middle east food/middle east food = falafel.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 FALAFEL mean?
FALAFEL noun- A Middle Eastern food in the form of balls made from chickpeas and other ingredients. Often served in a pita.
- A pita with falafel balls inside (like a sandwich or a wrap).
- A single falafel ball.