Dessert left out May's neighbour's tucked into in naive fashion (8)

I believe the answer is:

jejunely

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'dessert left out may's neighbour's tucked into' is the definition.
I can't tell whether this defines the answer.

'naive fashion' is the wordplay.
'naive' becomes 'jejune' (I've seen this in another clue).
'fashion' becomes 'ly' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'jejune'+'ly'='JEJUNELY'

'in' acts as a link.

Can you help me to learn more?

I've seen this clue in The Telegraph.

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