How steak might be served up, over a liquid containing last of chilli (2,6)

I believe the answer is:

au poivre

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'how steak might be' is the definition.
I don't know anything about this answer so I can't judge whether this works.

'up over a liquid containing last of chilli' is the wordplay.
'liquid' is an anagram indicator.
'containing' means one lot of letters goes inside another.
'last of' suggests the final letters.
The last letter of 'chilli' is 'i'.
'up'+'over'+'a'='upovera'
'upovera' anagrammed gives 'aupovre'.
'aupovre' enclosing 'i' is 'AU POIVRE'.

'served' acts as a link.

Can you help me to learn more?

(Another definition for au poivre that I've seen is " Peppered".)

I've seen this clue in The Times.

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