Prepare the barbecue for direct cooking over medium heat (180°C to 230°C).
While the barbecue is preheating, mix the sour cream, mayonnaise and coriander in a bowl, and season with salt and pepper. Rub the corn cobs with olive oil, salt and pepper.
Barbecue the corn cobs over direct medium heat, with the lid closed, until browned in spots and tender, 10 to 15 minutes, turning occasionally. Remove from the barbecue.
While the corn is still hot, coat with the coriander cream sauce on all sides. Squeeze fresh lime juice on the corn cobs and sprinkle with the parmesan.
Just before serving, finish with a light dusting of paprika and cayenne pepper.