Break up fog with a green concoction (5-3,4)

I believe the answer is:

split-pea soup

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'a green concoction' is the definition.
The answer and definition can be both things that one consumes for nourishment as well as being singular nouns.
Perhaps you can see a link between them that I don't see?

'break up fog' is the wordplay.
'break up' becomes 'split' (synonyms).
'fog' becomes 'peasoup' (pea soup is a kind of fog).
'split'+'peasoup'='SPLIT-PEA SOUP'

'with' is the link.

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I've seen this clue in The Guardian.

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