He presents with an abnormal sensation of his left hand that spreads to both his left arm and face. A lesion of the postcentral gyrus would cause this as it it responsible for sensation.

The deficit is purely sensory involving anatomic structures that are adjacent in the way they are mapped on our cortex. Think back to the sensory homunculus. What we are looking for here is the primary somatosensory cortex, which is located in the post central gyrus.