Heat the oil in a frying pan and lightly fry half of the onion and pointed peppers. Add half of the potatoes and fry for 3 - 4 minutes.
For the topping, whisk the eggs with the cream or milk. Stir in the parmesan and parsley and season with salt and pepper. Spread half of the well-mixed mixture over the vegetables in the frying pan and let it set over low heat for approx. 2 - 3 minutes. Turn the omelette with the help of a plate and fry the other side for approx. 2 minutes. Prepare the second omelette in the same way.