Boil the potatoes, peel them, and mash them while still hot. Add the eggs, pepper, salt, olive oil, and grated Parmigiano Reggiano. Mix well.
Spread half of the mixture in a previously oiled baking dish. Top with pieces of prosciutto and diced cheese, then cover with the remaining potato mixture.
For a golden crust, sprinkle the gateau with Parmigiano Reggiano, breadcrumbs, and a drizzle of olive oil.