Illegal hunter means to cook eggs? (7)

I believe the answer is:
poacher
'illegal hunter' is the definition.
(I've seen this before)
'to cook eggs?' is the wordplay.
'to cook' becomes 'poach' (poaching is a kind of cooking).
'eggs?' becomes 'er' (I can't justify this - if you can you should believe this answer much more).
'poach'+'er'='POACHER'
'means' is the link.
Can you help me to learn more?
(Other definitions for poacher that I've seen before include "Illegal catcher of game" , "Person hunting game illegally" , "criminal" , "in the kitchen?" , "One at the game" .)
