Metes out the Dover sole, not over cooked (5)

I believe the answer is:

doles

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'metes' is the definition.
(I've seen this in another clue)

'dover sole not over cooked' is the wordplay.
'not' suggests deleting specific letters.
'cooked' indicates anagramming the letters (letters cooked into a new form).
'dover'+'sole'='doversole'
'doversole' with 'over' taken out is 'dsole'.
'dsole' with letters rearranged gives 'DOLES'.

'out the' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Another definition for doles that I've seen is " Dishes out".)

I've seen this clue in the Evening Standard.

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