Wash and scrub carrots thoroughly with cold running water. Toss in a large dish with oil, salt, and pepper. Grill in batches, if necessary, on the rack of a covered grill directly over medium heat for 20 to 25 minutes or until tender, rolling carrots up and down the grill occasionally.
Stir together the yogurt, sour cream, rub, and 1/4 teaspoon kosher salt. Transfer carrots to a serving platter and top with yogurt mixture and pistachios.