Dice the tomato and bell pepper into small cubes and slice the spring onion into thin rings. Whisk the eggs with salt and pepper.
Heat the olive oil in a skillet over medium heat and briefly fry the bell pepper and the white part of the spring onion until they soften. Add the tomato and cook for another minute.
Pour the egg over the vegetables and let the omelet set gently; pull the edges toward the center occasionally. Scatter the green spring onion rings over the top and tear the basil over it. Fold the omelet in half or slide it flat onto a plate.