No-fault break-up: it might be what, say, Miley Cyrus and Liam Hemsworth had (3,4)

I believe the answer is:

nut loaf

'it might be what say miley cyrus and liam hemsworth had' is the definition.
(vegan snack)

'no-fault break-up' is the wordplay.
'break up' indicates an anagram.
'no'+'fault'='nofault'
'nofault' is an anagram of 'NUT LOAF'.

(Another definition for nut loaf that I've seen is " vegetarian dish".)

I've seen this clue in The Guardian.

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