Number-one cognitive quality (4-9)
I believe the answer is:
self-awareness
'number-one cognitive quality' is the definition.
I can't tell whether this definition defines the answer.
'number-one cognitive quality' is the wordplay.
'number one' becomes 'self' (I've seen this in another clue).
'cognitive' becomes 'aware' (I can't justify this - if you can you should believe this answer much more).
'quality' becomes 'ness' (I've seen this in other clues).
'self'+'aware'+'ness'='SELF-AWARENESS'
Can you help me to learn more?
(Another definition for self-awareness that I've seen is " Knowledge of one's own character".)