Rinse and peel the potatoes. Quarter the potatoes (cut them in half, then in half again). Cut the quarters in half again if they are large. Place the potato chunks into a large pot (6 quarts).
Add cold water to the pot, enough to cover the potatoes by one inch. (Starting with cold water instead of hot helps the potatoes cook evenly throughout.)
Place the pot over high heat on your stove. Add two teaspoons of salt to the water. Peel the garlic cloves, cut off the hard edges and add the cloves to the pot. Cover the pot, set a timer for 25 minutes, and let the pot come to a boil, making sure to remove the lid when the water is simmering, so the pot doesn't boil over. The potatoes are done when you can easily insert a fork in them; mine take 25-30 minutes, but it will depend on the size of your potato chunks. You will need to drain the potatoes in a colander in the sink when they are done cooking.
While the potatoes are cooking, shred the mozzarella and smoked mozzarella. Cut the salami into 1-inch pieces. Make the bread crumb mixture (see below.)
When the potatoes are done cooking, drain them and return them (and the two boiled garlic cloves) to your large pot. Preheat the oven to 375 degrees F.
Add six tablespoons of butter to the pot of potatoes and mash them with a potato masher. (I don't recommend using a ricer. See notes.) Add the milk to a microwave-safe measuring cup. (Use ½ cup + 2 tablespoons.) Warm up the milk in the microwave for 30 seconds at a time, just until it's warm, not hot.
Add the warmed milk to the potatoes, mashing and gently stirring to blend. Don't overmash them. Crack the egg into a cup or small bowl and beat it with a fork. Pour the beaten egg into the potatoes and add ½ teaspoon salt and ¼ teaspoon pepper. Stir to combine. The mixture should be smooth, with no lumps.
Stir in the salami, shredded mozzarella and smoked mozzarella.
Bread Crumb Mixture & Assembly
Add the bread crumbs, Parmesan, Pecorino, dried basil, pepper and salt to a small mixing bowl. Whisk to combine.
Grease a 9x13 baking dish with about two teaspoons of butter. (You can hold a stick of butter and rub it all over the bottom and sides of the pan.)
Place ½ cup of the bread crumb mixture into the greased pan. Tilt and shake the pan to distribute the crumbs to evenly coat the bottom of the pan.
Transfer the mashed potato mixture to the pan. Spread it evenly on top of the bread crumb coating.
Melt four tablespoons of butter in a glass measuring cup or microwave-safe bowl. (Place it in the microwave, lightly covered with wax paper, and heat it for 30 seconds, then an additional 20 seconds or more as needed.)
Stir the melted butter into the remaining bread crumb mixture. When the crumbs are evenly coated, place them on top of the potato casserole. Use a silicone spatula to spread the crumbs evenly over the entire surface.
Bake the gattò, uncovered, on the center rack for 25-30 minutes or until the top is crispy and golden brown, and the potatoes are bubbly. Let the casserole rest for 10 minutes before slicing it.
Refrigerate leftovers, tightly covered, for up to four days. To reheat, it's better to use the oven or a pan on the stove instead of the microwave. (See notes.)
Notes
Potatoes: Don't use red potatoes here, because they're too waxy and won't produce fluffy mashed potatoes.Use a masher: This recipe was developed using a potato masher. I don't recommend using a ricer here, because the potatoes would need extra butter and milk so they don't turn out dry.Salami: Genoa salami, which has peppercorns and a garlicky flavor, is softer than hard salami and works better in this dish.To ReheatFor the best texture, reheat the potatoes in the oven or on the stove instead of in the microwave. Oven: Reheat the Italian gattò at 350 degrees F, covered with foil. Start with 15 minutes and see if it needs more time.Stovetop: Place slices of the casserole in a skillet over medium-low heat and cover the pan with a lid. Heat the potatoes for 10 minutes or until they're warmed through.To FreezeFreeze the potato casserole after it has cooled off from baking. Cut it into portions and freeze them in a freezer bag for up to two months.Thaw the frozen gattò in the refrigerator overnight. Reheat it in the oven or on the stove, as described in the previous section.