Italian pastry No. 1 clan cooked (7)

I believe the answer is:

cannoli

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'italian pastry' is the definition.
I don't know anything about this answer so I cannot tell whether it can be defined by this definition.

'no 1 clan cooked' is the wordplay.
'1' becomes 'i' (roman numeral).
'cooked' is an anagram indicator.
'no'+'i'+'clan'='noiclan'
'noiclan' with letters rearranged gives 'CANNOLI'.

Can you help me to learn more?

(Another definition for cannoli that I've seen is " Dessert".)

I've seen this clue in The Hindu.

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