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Pasta produced by jazz bar with duck took off over in California (9)

Ross

I believe the answer is:

carbonara

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'pasta produced by jazz' is the definition.
I know nothing about this answer so I cannot tell whether it can be defined by this definition.

'bar with duck took off over in california' is the wordplay.
I cannot quite understand how this works, but
an anagram of 'bar' is 'arb' which is located in the answer.
'duck' could be 'o' (resembles zero - 'duck' in cricket) and 'o' is found in the answer.
'california' could be 'c' and 'c' is present in the answer.
The remaining letters 'nara' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Another definition for carbonara that I've seen is " Type of pasta sauce".)

I've seen this clue in The Irish Times.
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