When the oil is hot, fry the onions until almost transparent, around 2-3 minutes. Mix in the red pepper, and cook for another minute. Add in the kale, and cook until the kale is wilted, 3-4 minutes.
Meanwhile, beat the eggs, salt and pepper in a small bowl until smooth. Pour on top of the vegetables, and turn the pan to coat skillet with egg. Turn after the omelette is golden brown, around 3 minutes. Cook for another 3 minutes and turn onto a plate.