The most common and most likely answer to this crossword clue is the 11 letter word RHAPSODISED
R
H
A
P
S
O
D
I
S
E
D
Buddy explains!

The straight part
We know that "Wrote with great enthusiasm/an" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case wrote with great enthusiasm/an = rhapsodised.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 RHAPSODISED mean?
RHAPSODISED verb- To speak with exaggerated or rapturous enthusiasm (about, (up)on or over something).
- To say (something) with exaggerated or rapturous enthusiasm.
- To recount or describe (something) as a rhapsody, or in the manner of a rhapsody.
- To perform a rhapsody.