In a small bowl, mix the tomato, cheese, basil, onion, half of the oil, and some salt and pepper together.

Heat remaining oil in a small frying pan and pour in an even layer of the eggs. Once cooked, spoon tomato mixture over half of the omelette, and fold the other half of the omelette over it.

Keep on the heat for another 30 seconds or so and then remove and plate.