Crossword Genius

Average place to get food cut short a new cheese (8)

Ross

I believe the answer is:

parmesan

I'm a little stuck... Click here to teach me more about this clue!

'cheese' is the definition.
(Parmesan is an example)

'average place to get food cut short a new' is the wordplay.
I cannot really understand how this works, but
'average' could be 'par' (I've seen this before) and 'par' is found in the answer.
'food' could be 'e' (E is an example) and 'e' is located in the answer.
'a' could be 'an' and 'an' is found within the answer.
The remaining letters 'ms' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for parmesan that I've seen before include "that grates", "Dry sharp-flavoured Italian cheese", "Hard dry cheese, often grated", "Spearman (anag) - cheese", "that's grated".)

I've seen this clue in The Hindu.
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