Cut the potatoes into quite small evenly sized pieces ( so with a small potato cut in half). Heat up the oil in a medium sized frying pan. Add the onion and potatoes and sprinkle with salt and pepper.
Cover the pan and cook the vegetables slowly in the oil, stirring occasionally. After about 15 minutes, when the potatoes are becoming tender, beat the eggs together in a bowl.
Lift the cooked vegetables from the pan using a slotted spoon, leaving behind as much oil as possible. Stir the vegetables into the eggs.
Clean the pan if very encrusted, otherwise pour off enough oil to just leave the base covered. Pour the egg mixture into the pan and cook gently, shaking from time to time until the base is set. Then put the omelette under the grill to brown the top.