The most common and most likely answer to this crossword clue is the 13 letter word INTROSPECTION
I've seen this crossword clue in The Guardian
I
N
T
R
O
S
P
E
C
T
I
O
N
More clues leading to the result INTROSPECTION
- Brooding opening piece, involving piano
- Soul-searching pub hosts stop erotic dancing
- Opening piece must include quiet contemplation
- I contort spine awkwardly for self-examination
- Poetic sort in troubled new soul-searching
- Looking inside with interest, Ron nearly bumps into chief of police entering precinct
Buddy explains!

The straight part
We know that "Brooding" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case brooding = introspection.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 INTROSPECTION mean?
INTROSPECTION noun- A looking inward; specifically, the act or process of self-examination, or inspection of one's own thoughts and feelings; the cognition which the mind has of its own acts and states
- The ability of a program to examine at run time the type or properties of an object.