Eagerly sought last of crumble in bowl (5)

I believe the answer is:

wooed

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'eagerly sought' is the definition.
'wooed' can be an answer for 'sought' (I've seen this in another clue). I am not certain of the 'eagerly' bit.

I don't understand the rest of the clue.

Can you help me to learn more?

(Other definitions for wooed that I've seen before include "Sought the love of" , "Courted" , "Pursued" .)

I've seen this clue in The Sunday Times and The Times.

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