Crossword Genius

Expert introducing baked item from each one (6)

Ross

I believe the answer is:

apiece

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'from each one' is the definition.
(synonyms)

'expert introducing baked item' is the wordplay.
'expert' becomes 'ace' (ace can informally mean very good).
'introducing' indicates putting letters inside (some letters introduced or inserted into others).
'baked item' becomes 'pie' (I can't explain this - if you can you should give a lot more credence to this answer).
'ace' going around 'pie' is 'APIECE'.

Can you help me to learn more?

(Other definitions for apiece that I've seen before include "for everyone" , "Per person" , "For or by each one of group" , "A head" .)

I've seen this clue in The Times.
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