Parmesan exemplifies bad luck (4,6)

I believe the answer is:
hard cheese
'luck' is the definition.
(I have seen 'Bad luck ' mean 'hard cheese' so perhaps 'luck' could also mean 'hard cheese')
'parmesan exemplifies bad' is the wordplay.
I cannot quite understand how this works, but
'bad' could be 'hard' (similar in meaning) and 'hard' is present in the answer.
The remaining letters 'cheese' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for hard cheese that I've seen before include "Expression of sympathy" , "commiserating words" , "mousetrap" , "Che sfortuna!" , "Leicester" .)
