- Heat gas grill to high. Combine mayonnaise, cheese, garlic, basil, and paprika in very large bowl or baking dish.
- Brush corn with oil and season with salt and pepper.
- Grill corn with lid down, turning occasionally, until charred on all sides, 8–10 minutes.
- Quickly transfer to bowl with mayonnaise mixture and toss to coat. Serve immediately, sprinkled with additional basil.