Part of food processor in a mess, little pumpkin ultimately churned up (5,9)

I believe the answer is:

small intestine

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

'part of food processor' is the definition.
'small intestine' can be an answer for 'part' (small intestine is a kind of part). I am unsure of the 'of food processor' bit.

'in a mess little pumpkin ultimately churned up' is the wordplay.
'ultimately' suggests the final letters.
'churned up' indicates anagramming the letters (letters churned or mixed up).
The final letter of 'pumpkin' is 'n'.
'in'+'a'+'mess'+'little'+'n'='inamesslittlen'
'inamesslittlen' anagrammed gives 'SMALL INTESTINE'.

Can you help me to learn more?

(Other definitions for small intestine that I've seen before include "part of the body" , "Outlet from the stomach" .)

I've seen this clue in The Telegraph.

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