Kill me? How? Possibly with a drink with maximum fat (5,4)

I believe the answer is:

whole milk

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'a drink with maximum fat' is the definition.
I can't tell whether this definition defines the answer.

'kill me? how? possibly' is the wordplay.
'possibly' indicates an anagram.
'kill'+'me'+'how'='killmehow'
'killmehow' anagrammed gives 'WHOLE MILK'.

'with' is the link.

Can you help me to learn more?

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

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