Preheat oven to 425 degrees. In a medium saucepan, combine potatoes and 1 teaspoon salt. Add water to cover. Bring to a boil over high heat. Cook until potatoes are tender, about 15 minutes. Drain, and set aside.

In a large ovenproof nonstick skillet, heat oil and butter over medium heat. Add onions, and cook until translucent, about 5 minutes. Add potatoes, and cook for 5 minutes more.

In a large bowl, whisk together eggs, the remaining teaspoon of salt, and pepper. Add parsley, if desired. Add egg mixture to skillet, and cook, drawing eggs away from the sides and bottom of the pan with a heatproof spatula so that the uncooked egg runs underneath. When the mixture is loosely set around the edges, place pan in the oven, and bake until puffed and completely set, about 20 minutes. Remove pan from the oven and slide out onto a serving plate.