Birds greedily eat one's nuts (7)

I believe the answer is:

pigeons

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'birds' is the definition.
(pigeon is a kind of bird)

'greedily eat one's nuts' is the wordplay.
'greedily eat' becomes 'pig' (pigging is a kind of eating. I am not sure about the 'greedily' bit.).
'nuts' indicates an anagram (nuts can mean crazy).
'ones' anagrammed gives 'eons'.
'pig'+'eons'='PIGEONS'

Can you help me to learn more?

(Other definitions for pigeons that I've seen before include "Type of type or nose" , "Town birds" , "Columbiform birds" , "traditional pie filling" , "Cooing birds" .)

I've seen this clue in The Telegraph.

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