Although I haven't read the Australian children's book "The Magic Pudding", I'm familiar with the phrase "cut and come again" being used in it.
Is the phrase understood outside of Australia?
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Yes, the phrase, 'cut-and-come-again' is definitely used in the UK, usually to refer to types of vegetable or yummy chocolate cakes.
Here are some definitions:
'It was cut, roast, and come again, for the next hour and a half.'
Source: Fine Dictionary
Examples of usage from the UK: