Greek character with endless salt served up type of American cuisine (5)
I believe the answer is:
cajun
'greek character' is the definition.
The answer and definition can be both people as well as being singular nouns.
Perhaps you can see a link between them that I don't see?
'endless salt served up type of american cuisine' is the wordplay.
'endless' says to take the centre.
'salt' becomes 'NaCl' (NaCl is the chemical formula for sodium chloride).
'served up' is a reversal indicator (in a down clue, going upwards).
'type of american cuisine' becomes 'jun' (I can't justify this - if you can you should believe this answer much more).
The middle of 'nacl' is 'ac'.
'ac' written backwards gives 'ca'.
'ca'+'jun'='CAJUN'
'with' acts as a link.
Can you help me to learn more?
(Other definitions for cajun that I've seen before include "Louisianan of French Canadian descent" , "Type of Louisiana food" , "One of the 9 [BAYOU] people" , "Native of Louisiana descended from 18th-century Acadian immigrants" , "French-speaking Louisiana native" .)