Place corn on the rack of a gas or charcoal grill. Cover and cook over direct medium-high heat until lightly charred, turning occasionally, 8 to 10 minutes. Remove from the grill. Let cool until easy to handle.

Cut kernels from the cobs; discard cobs. Combine corn kernels and pesto in a large bowl; stir to coat.

Transfer to a serving dish. Top with Parmesan cheese, basil, lemon zest, and cracked black pepper.