Add the potato and onion. Cover and cook gently for 20 minutes until softened.
While the potato and onion are cooking, beat the eggs in a large bowl.
Remove the potatoes and onions from the pan with a slotted spoon and add them to the beaten eggs. Add pepper to taste.
Heat the pan again over a high heat and add the egg mixture. Cook for 2-3 minutes.
Place a plate over the pan. Tip the pan upside down so the omelette lands on the plate. Then slide the omelette back into the pan and cook the other side for a further 5 minutes until golden brown but moist in the middle.