In a nonstick skillet on medium heat, add oil, potatoes, onions, 1 teaspoon salt and 1/2 teaspoon pepper. Cook potatoes just until tender, do not let them break.
In a large bowl, whisk eggs, parsley, remaining salt and pepper. Remove potatoes from skillet into egg mixture and gently toss. Pour mixture back into skillet.
With a rubber spatula pull the eggs away from the sides of the pan, moving the egg mixture around. Let cook for 5 to 7 minutes on medium heat, then flip tortilla over to cook underside. Push sides of tortilla into itself, this will lift the tortilla slightly. Cook for another 5 minutes on low heat.
Slide onto cutting board. Top with prosciutto. Cut into 6 pieces. Serve immediately.