The most common and most likely answer to this crossword clue is the 9 letter word CROISSANT
I've seen this crossword clue in The Times
C
R
O
I
S
S
A
N
T
More clues leading to the result CROISSANT
- Mule maybe swallowing one insect for breakfast?
- Accompanied by worker, one tucked into crusty roll
- Annoyed about one insect in pastry
- Arsonist caught making something to eat
- Angry worker eating one pastry
- Annoyed about one bug found in French roll
- Co-star is devastated about new role
- Worker perhaps after middle of shift tucked into crusty item from bakery
- Bread roll crusty? Worker consumes one
- Sort out 1 across before finishing bran and toast for breakfast, perhaps
Buddy explains!

The straight part
We know that "pastry" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case pastry = croissant.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 CROISSANT mean?
CROISSANT noun- A flaky roll or pastry in a form of a crescent.