Working into the night, making Bourdain’s third dish (2,4)

I believe the answer is:

up late

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'working into the night' is the definition.
I know nothing about this answer so I cannot tell whether this works.

'bourdain's third dish' is the wordplay.
'bourdain's third' becomes 'u' (3rd letter of 'bourdain').
'dish' becomes 'plate' (plate is a kind of dish).
'u'+'plate'='UP LATE'

'making' acts as a link.

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I've seen this clue in the Sydney Morning Herald.

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