Finished with a type of Italian food (5)

I believe the answer is:

pasta

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'italian food' is the definition.
(type of Italian food)

'finished with a' is the wordplay.
'finished with' becomes 'past' (past can mean forgotten or finished).
'past'+'a'='PASTA'

'type of' acts as a link.
This may not be correct. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for pasta that I've seen before include "Staple food of Italy" , "Italian foodstuff" , "Shaped and dried dough" , "E.g. fusilli" , "Linguine, e.g." .)

I've seen this clue in The Daily Express.

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