In a small bowl, beat the eggs and season with salt and pepper.
In a small skillet, heat the olive oil over medium heat. Pour the eggs into the skillet and cook undisturbed until just set, 1 to 2 minutes. Use a spatula to loosen the edges of the omelette, and tilt the pan slightly to move any unset egg to the surface.
When the surface of the omelette is barely moist, scatter the tomatoes and onion over the top.
Cover the pan, reduce the heat to low, and continue to cook for 1 minute. Remove the pan from the heat and let the omelette rest for about 1 minute, covered. Sprinkle with the basil and serve.