Give a little brushing with oil, and cook (5)

I believe the answer is:

broil

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'cook' is the definition.
(I know that broil is a more specific form of the action grill)

I don't understand the remainder of the clue.

(Other definitions for broil that I've seen before include "Maybe grill" , "Be extremely hot" , "cook?" , "disturbance" , "stew" .)

I've seen this clue in the Evening Standard.

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