The most common and most likely answer to this crossword clue is the 4 plus 9 letter word ROOT VEGETABLE
I've seen this crossword clue in Financial Times
R
O
O
T
V
E
G
E
T
A
B
L
E
More clues leading to the result ROOT VEGETABLE
Buddy explains!

The straight part
We know that "Food" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case food = root vegetable.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.