Light a large chimney started filled with charcoal (about 6 quarts) and allow to burn until the coals are partially covered with a layer of ash, about 20 minutes.
Build a modified two-level fire by arranging all the coals over half of the grill, leaving the other half empty. Set the cooking grate in place, cover, and heat the grate until hot, about 5 minutes. Use a grill brush to scrape the cooking grate clean. Dip a wad of paper towels in vegetable oil holding the wad with tongs, oil the cooking grate (we just used Pam for grilling and sprayed it on the grate while it was suspended in the air with tongs - away from the flames!)
Meanwhile, combine the cheese, mayonnaise, sour cream, basil, lemon juice, garlic, pepper, and salt in a large bowl. Add corn and toss to coat evenly.
Grill the corn until lightly charred on all sides, 7 to 12 minutes total. Serve immediately.