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1
Place the whole, unpeeled floury potatoes in a pot of cold salted water. Bring to the boil and cook until a skewer meets no resistance at the centre — the potatoes are completely tender.
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2
Drain immediately. Peel while still hot, handling with a cloth, then pass through a potato ricer or mouli into a wide bowl. Work in the butter first, then the egg yolks, grated Parmigiano, and warmed milk. Season with salt and pepper. The purée should be rich, supple, and slightly looser than table mashed potato — baking will firm it. Taste: it should seem almost too well-seasoned.
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3
Heat the oven to 180 °C. Butter a baking dish generously, then coat every surface evenly with breadcrumbs, tapping out the excess. This is where the dish lives or dies: an under-buttered, under-crumbed dish will surrender its crust to the pan, and the signature shattering exterior will not form.
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4
Spread half the potato purée in an even layer across the base of the prepared dish, smoothing it with a spatula to reach the edges.
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5
Distribute the cubed provola affumicata, salame or mortadella, cubed prosciutto cotto, and hard-boiled egg slices if using, evenly across the potato layer. No portion of the dish should be without filling.
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6
Cover with the remaining potato purée, smoothing the top flat. Scatter breadcrumbs and grated Parmigiano evenly over the surface; dot with small pieces of cold butter.
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7
Bake at 180 °C for 30 to 40 minutes. The dish is ready when the top crust is deep golden and the edges have pulled slightly from the sides of the dish — the smell of rendered salame fat and toasted cheese will be pronounced.
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8
Remove from the oven and rest for at least ten minutes before cutting. Tap the crust with the back of a spoon: it should sound firm and hollow. Cut in portions and serve — the provola will stretch in long strings when the portion is lifted.