Grocer's unfilled piece of cake was fatty (6)

I believe the answer is:

greasy

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'fatty' is the definition.
(synonyms)

'grocer's unfilled piece of cake' is the wordplay.
'grocer's unfilled' becomes 'gr' (I can't explain this - if you can you should believe this answer much more).
'piece of cake' becomes 'easy' (I've seen this before).
'gr'+'easy'='GREASY'

'was' acts as a link.

Can you help me to learn more?

(Other definitions for greasy that I've seen before include "Cheap 24" , "Unctuous, being lubricated" , "Sticky with fat" , "Covered with fat" , "Thickly oleaginous" .)

I've seen this clue in the Sydney Morning Herald.

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