Cook's utensil encourages vermin (3,5)
I believe the answer is:
egg slice
'cook's utensil' is the definition.
'encourages vermin' is the wordplay.
'encourages' becomes 'eggs'.
'vermin' becomes 'lice'.
'eggs'+'lice'='EGG SLICE'
(Another definition for egg slice that I've seen is " Kitchen utensil".)
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