New Orleans cooking style (5)
I believe the answer is:
cajun
'new orleans cooking style' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for cajun that I've seen before include "Of folk music (or spicy cuisine) from southern Louisiana" , "French dialect of Louisiana" , "spicy food like this?" , "Type of Louisiana food" , "Louisianan of French Canadian descent" .)