The cook . . . . . . . . cooking food at this time tomorrow.

Answer: Option B

To determine the correct form of the verb we have to see the below facts-
After third person will always use 'will'. Here the noun 'the cook' is a third-person so, 'will' will be used.
After will the simple form of the verb is used but there 'cooking' is given so, the correct form is 'will be'.