Shave the corn off the cobs into a bowl with a sharp knife. Set the sweetcorn aside.
Break the cobs in half and place them in a large saucepan. Add 1.5L water and bring to the boil. Reduce the heat, cover and simmer for 15 minutes. Strain and reserve the broth. Discard the cobs.
Heat the butter in the saucepan. Add the onion and fry until translucent. Add the pepper and chilli and cook, stirring, until the peppers start so soften, about 5 minutes. Add the sweetcorn, salt and smoked paprika and bring to the boil. Reduce the heat, cover and simmer until the peppers are very soft, about 15 minutes.
Briefly puree the soup with a stick blender so it is thickened but still chunky. Stir in a generous gulp of double cream and season with smoked pepper, salt and pepper to taste. Serve hot with basil on each plate.