The most common and most likely answer to this crossword clue is the 9 letter word BAKEHOUSE
I've seen this crossword clue in The Times
B
A
K
E
H
O
U
S
E
Buddy explains!
The straight part
We know that "food establishment" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case food establishment = bakehouse.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 BAKEHOUSE mean?
BAKEHOUSE noun- A building or an apartment used for the preparing and baking of bread and other baked goods.
- A building principally containing ovens.
- Bakery.