Prepare grill for medium heat.
Grill corn, turning occasionally, until tender and charred, 8-10 minutes; let cool slightly. Cut kernels from cobs and transfer to a medium bowl.
Whisk mayonnaise, lime juice, paprika, cayenne (if using), 2 ounces Cotija cheese, and 2 tablespoons cilantro in a large bowl; season with salt and pepper. Dressing can be made 2 days ahead; cover and chill in refrigerator until ready to use.
Add corn and toss to combine. Top with more cheese and cilantro.