Separate the whites from the yolks and beat the egg whites in a glass or stainless steel bowl until they form peaks. Season the egg yolks before folding them through the beaten egg white. Preheat the grill.
Heat the olive oil in a non stick omelette pan until quite hot. Add the shredded basil and chili until the basil turns dark green. Remove the from the pan and set aside. Add the egg to the pan spreading the mixture across the whole base and cook for approx 3 - 4 minutes easing it gently from the sides of the pan. Drop the basil, chilli and cheese onto the surface then cook the top of the omelette under the grill for a further 3 - 4 minutes.