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Peel back the corn husks, then trim away using a sharp knife and discard. Bring a large pan of salted water to the boil, lower the heat to medium and cook the corn cobs for 10 mins. If you’ll be cooking the corn in a frying pan instead of the barbecue, cook for 13 mins.
Meanwhile, make the paprika & lime butter. Mix the softened butter with the paprika until fully combined. Stir in half the lime zest and half the parmesan.
Light the barbecue, if using, and wait until the coals are ashen. Alternatively, heat a dry frying pan over a medium heat until hot. Drain the corn, pat dry with kitchen paper and brush lightly with the oil. Cook for 7-10 mins in the hot pan or on the barbecue, turning every couple of minutes until golden and slightly charred in spots.
Remove the corn to a plate using tongs and spread the paprika butter all over it. Sprinkle with the rest of the parmesan, the coriander and the remaining lime zest. Serve with the lime halves for squeezing over.