Crossword Genius

Peaked cap, which may divide Derby or Cheshire? (12)

Ross

I believe the answer is:

cheesecutter

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

'peaked cap' is the definition.
'cheesecutter' can be an answer for 'cap' (I've seen this before). I am unsure of the 'peaked' bit.

'may divide derby or cheshire?' is the wordplay.
I cannot quite see how this works, but
'divide' could be 'cut' (cutting is a kind of dividing) and 'cut' is found within the answer.
'cheshire?' could be 'cheese' (I've seen this before) and 'cheese' is found within the answer.
The remaining letters 'ter' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

'which' acts as a link.

Can you help me to learn more?

(Another definition for cheesecutter that I've seen is " Cap".)

I've seen this clue in The Telegraph.
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