Heat 2 tablespoons of the oil in a small heavy-based frying pan that's about 20cm/8in in diameter. Add the onion and fry for 5 minutes.
Add the pepper and potatoes and season with salt and pepper. Cover with a lid and gently cook over a low heat for about 15–20 minutes, or until the vegetables are soft and the potatoes are cooked through. Transfer to a bowl and wipe the pan clean.
Beat the eggs in a bowl and season with salt and pepper. Pour the eggs into the bowl with the cooked mixture.
Add the remaining oil to the pan. Carefully pour in the egg mixture and sprinkle with parsley. Cook on a medium heat until the sides and top have just set and the base is lightly golden-brown. When the middle is set, carefully slide onto a plate.
Put the pan on top of the omlette and flip over to cook the other side for 3–4 minutes, or until golden-brown all over and just cooked through. Slide onto a plate to serve.