The most common and most likely answer to this crossword clue is the 16 plus 7 letter word BREAD-AND-BUTTER PUDDING
I've seen this crossword clue in The Times
B
R
E
A
D
-
A
N
D
-
B
U
T
T
E
R
P
U
D
D
I
N
G
Buddy explains!
The straight part
We know that "sweet" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sweet = bread-and-butter pudding.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.