The most common and most likely answer to this crossword clue is the 9 letter word CLAFOUTIS
I've seen this crossword clue in Independent
C
L
A
F
O
U
T
I
S
Buddy explains!

The straight part
We know that "fruit dessert" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fruit dessert = clafoutis.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 CLAFOUTIS mean?
CLAFOUTIS noun- A French dessert made by baking fresh fruit (traditionally cherries) with a batter.