Cut the potatoes in 1-inch pieces. Place in a medium skillet along with the onion and bell pepper. Add 1 teaspoon salt and pour in enough water to just cover the vegetables, Bring to a boil over high heat. Reduce to a simmer, cover the pan and let cook for 10 minutes or until the potatoes are tender.
Drain off the water, add the oil and ham and stir. Let cook over high heat, stirring once or twice, for 2 minutes. Whisk the eggs with ½ teaspoon salt and ½ teaspoon pepper. Reduce the heat to low, add the eggs and let cook, stirring occasionally, until the eggs are set, about 5 minutes. Serve immediately.