Brainy part, cooking eel crumble (10)

I believe the answer is:

cerebellum

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'brainy part' is the definition.
'cerebellum' can be an answer for 'part' (cerebellum is a kind of part). I'm unsure of the 'brainy' bit.

'cooking eel crumble' is the wordplay.
'cooking' is an anagram indicator (cook can mean to falsify or distort).
'eel'+'crumble'='eelcrumble'
'eelcrumble' anagrammed gives 'CEREBELLUM'.

Can you help me to learn more?

(Other definitions for cerebellum that I've seen before include "motor controller" , "bit of brain" , "part of the brain" .)

I've seen this clue in The Daily Express.

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