Begin by peeling the potatoes and slicing them into thin rounds, about ¼ inch thick.
In a large skillet, heat the extra virgin olive oil over medium heat. Add the sliced potatoes and season with a pinch of sea salt. Cook for about 10-15 minutes, stirring occasionally, until they are tender and lightly golden.
While the potatoes are cooking, crack the eggs into a mixing bowl. Whisk until fully combined, then stir in the chopped parsley, grated cheese (if using), and season with salt and pepper.
Once the potatoes are cooked, reduce the heat to low. Pour the egg mixture over the potatoes, ensuring it spreads evenly. Allow to cook undisturbed for about 5-7 minutes, or until the edges start to set.
To cook the top of the frittata, place the skillet under a broiler for a couple of minutes or cover with a lid and let cook on low heat until fully set, about 5 minutes.
Once cooked through, let cool for a few minutes. Slice into wedges and serve warm or at room temperature, garnished with additional parsley if desired.