Leafy green – or cheese and white wine? Not half! (5,5)

'not half' is the definition.
Although both the answer and definition are singular nouns, I don't understand how they can define each other.

'leafy green or cheese and white wine?' is the wordplay.
I cannot quite understand how this works, but
'green' could be 'chard' (chard is a kind of green) and 'chard' is found within the answer.
'cheese' could be 'swiss' (Swiss cheese is an example) and 'swiss' is located in the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?