Audibly bemoan making cooking mixture (4)
I believe the answer is:
roux
'cooking mixture' is the definition.
(fat mixture used in cooking)
'audibly bemoan' is the wordplay.
'audibly' indicates a 'sounds like' (homophone) clue.
'bemoan' becomes 'rue' (I've seen this before).
'rue' is a homophone of 'ROUX'.
'making' is the link.
(Other definitions for roux that I've seen before include "Fat and flour mixture, cooked and used to make sauces" , "Butter and flour sauce combination" , "Mixture of fat and flour used for thickening sauces" , "Fat, flour sauce base" , "sauce mix" .)