Puff up aged grains after cooking (10)
I believe the answer is:
aggrandise
'puff up' is the definition.
'aged grains after cooking' is the wordplay.
'after cooking' indicates an anagram.
'aged'+'grains'='agedgrains'
'agedgrains' is an anagram of 'AGGRANDISE'.
(Other definitions for aggrandise that I've seen before include "Give promotion to" , "Advance" , "Magnify; increase power of" .)