Put the potatoes in boiling water. Bring back to the boil, then reduce the heat to a simmer. Add the chopped capsicums and simmer for 3 minutes. Drain well, then cover and keep hot.
Heat a 25cm (10in) nonstick frying pan over high heat. Add oil to the pan and swirl around. When the oil is hot, reduce the heat to medium. Add the onion and sauté, stirring often, for about 3 minutes or until softened.
Add the potatoes, capsicum and sweetcorn. Continue sautéing, stirring and turning the vegetables, for about 8 minutes or until the potatoes are tender. Remove the pan from the heat.
In a large bowl, beat the eggs with the parsley and pepper to taste. Use a slotted spoon to add the vegetables to the eggs, stirring them in thoroughly. (If any vegetables have stuck to the bottom of the pan, thoroughly clean and dry the pan before heating it with an additional 1 tbsp oil; however, this should not be necessary with a reliable nonstick pan.)
Replace the pan, with the oil remaining from cooking the vegetables, over a moderate heat. When the pan is hot, pour in the egg mixture, spreading out the vegetables evenly. Cook the frittata, shaking the pan frequently, for 3–4 minutes or until the edges are set and the top is beginning to look set.
Meanwhile, preheat the grill to the hottest setting. Place the frittata under the grill and cook for 2 minutes or until the top is just set. Pierce the top of the frittata with a knife to check that it is cooked through.
Remove the pan from under the grill and leave the frittata to set for 2 minutes, then slide it on to a serving plate. Serve hot or at room temperature, cut into wedges.
NOTE: The trick for a perfect frittata is to cook over a medium to low heat and allow the mixture to set slowly without stirring. Stirring once the egg has begun to set will break the mixture apart. Too high a heat will burn the base before the egg is set sufficiently to finish under the grill.