Mexican-Style Grilled Corn

1A. FOR A CHARCOAL GRILL: Open bottom vent completely. Light large chimney starter filled with charcoal briquettes (6 quarts). When top coals are partially covered with ash, pour evenly over half of grill. Set cooking grate in place, cover, and open lid vent completely. Heat grill until hot, about 5 minutes.
1B. FOR A GAS GRILL: Turn all burners to high, cover, and heat grill until hot, about 15 minutes.
2. Meanwhile, combine Pecorino, mayonnaise, sour cream, cilantro, lime juice, garlic, 1⁄4 teaspoon chili powder, pepper, and cayenne, if using, in large bowl and set aside. In second large bowl, combine oil, salt, and remaining 1⁄2 teaspoon chili powder. Add corn to oil mixture and toss to coat evenly.
3. Clean and oil cooking grate. Place corn on grill (hot side if using charcoal) and cook (covered if using gas) until lightly charred on all sides, 7 to 12 minutes, turning as needed. Place corn in bowl with cheese mixture, toss to coat evenly, and serve.