Wash and cut the potato into very thin slices. Heat a frying pan with some olive oil. Arrange the potato slices in a ring pattern. Sprinkle on the parmesan cheese. Cover and cook on low heat for 5 minutes.
Spread the tomato sauce onto the potatoes. Arrange mushroom slices and mozzarella cheese on top. Crack an egg into the center. Cover and cook on medium heat for 5 minutes.
Transfer the potato pizza onto a plate and place sheets of prosciutto on top. Serve with a drizzle of olive oil and black pepper.