Men go in lift possibly to get what restaurant offers? (5,6)

I believe the answer is:

filet mignon

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'get what restaurant offers?' is the definition.
I can't judge whether this definition defines the answer.

'men go in lift possibly' is the wordplay.
'possibly' indicates anagramming the letters.
'men'+'go'+'in'+'lift'='mengoinlift'
'mengoinlift' with letters rearranged gives 'FILET MIGNON'.

'to' acts as a link.

Can you help me to learn more?

(Other definitions for filet mignon that I've seen before include "steak" , "Tender piece of beef" , "Small tender boneless cut of beef" .)

I've seen this clue in The Times.

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