Crossword Genius

Prominent figure with concern about end of luncheon after cold dish (6,3,5)

Ross

I believe the answer is:

chilli con carne

I'm a little stuck... Click here to teach me more about this clue!

'dish' is the definition.
(I've seen this before)

'prominent figure with concern about end of luncheon after cold' is the wordplay.
I cannot quite see how this works, but
'figure' could be 'icon' (I've seen this in another clue) and 'icon' is found in the answer.
'about' could be 'ca' (abbreviation for 'circa') and 'ca' is present in the answer.
'cold' could be 'chill' (chill can mean cold) and 'chill' is located in the answer.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for chilli con carne that I've seen before include "fare" , "meal" , "Spicy stew" , "Spicy dish" .)

I've seen this clue in The Times.
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