Fish extra tasty essentially in small portion (5,4)

I believe the answer is:

dover sole

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'fish' is the definition.
(type of fish)

'extra tasty essentially in small portion' is the wordplay.
'extra' becomes 'over' (both can mean left over).
'essentially' means to look at the middle letters.
'in' is an insertion indicator.
'small portion' becomes 'dole' (dole is a kind of portion. I am not sure about the 'small' bit.).
The centre of 'tasty' is 's'.
'over'+'s'='overs'
'overs' inserted inside 'dole' is 'DOVER SOLE'.

Can you help me to learn more?

(Other definitions for dover sole that I've seen before include "Catch" , "Kentish flat fish" .)

I've seen this clue in The Times.

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