Repeatedly question cook (5)
I believe the answer is:
grill
This clue is a double definition.
'repeatedly question' is the first definition.
(grill can mean to question aggressively)
'cook' is the second definition.
(grilling is a form of cooking)
(Other definitions for grill that I've seen before include "Cook by radiant heat" , "rack" , "Broil" , "Cooking device" , "keep on with questions?" .)