Boring count may provide some intelligence (4,6)
I believe the answer is:
grey matter
'some intelligence' is the definition.
(I've seen this before)
'boring count' is the wordplay.
'boring' becomes 'grey' (I can't explain this - if you can you should give a lot more credence to this answer).
'count' becomes 'matter' (synonyms).
'grey'+'matter'='GREY MATTER'
'may provide' acts as a link.
Can you help me to learn more?
(Other definitions for grey matter that I've seen before include "Brains" , "intellectual capacity?" , "Brain tissue" , "stuff in the head" , "Issue lacking clear boundaries" .)