Old chip halved inside cheese roll (7)
I believe the answer is:
'roll' is the definition.
(brioche is a kind of roll)
'old chip halved inside cheese' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'halved' suggests halving the letters.
'inside' indicates putting letters inside.
'cheese' becomes 'brie' (Brie is an example).
'chip' halved is 'ch'.
'och' inserted into 'brie' is 'BRIOCHE'.
(Other definitions for brioche that I've seen before include "Soft roll made of light yeast dough", "Idol", "Hire cob (anag) - bread", "Type of light soft roll", "Sweet yeast bread".)