Crossword Genius

Infallible pudding and what comes with its eating? (9)

Ross

I believe the answer is:

foolproof

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

'infallible' is the definition.
(similar in meaning)

'pudding and what comes with its eating?' is the wordplay.
I cannot really see how this works, but
'pudding' could be 'fool' (type of dessert) and 'fool' is found in the answer.
The remaining letters 'proof' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for foolproof that I've seen before include "Certain" , "Infallible" , "sure to work" , "incapable of going wrong" , "Not admitting failure" .)

I've seen this clue in The Times.
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