Place cubed potatoes in a large pot with enough cool water to cover by 2 inches. Add a pinch of salt, bring to a boil, reduce heat, and simmer until potatoes are soft, about 15 minutes. (You can also cook the potatoes in a pressure cooker according to your manufacturer's directions.) Drain potatoes well in a colander and let stand 5 minutes.
Preheat oven to 425 degrees F (standard) or 400 degrees F (convection).
In a large bowl, pass potatoes through a food mill or ricer, or mash well with a masher. Stir in softened butter with a wooden spoon until melted and combined. Add heavy cream, 1/2 cup grated Parmigiano Reggiano, salt, pepper, and nutmeg. Adjust salt and pepper to taste. Add egg yolks, one at a time, stirring until incorporated. Transfer potato mixture to a pastry bag fitted with a large star tip.
Line two baking sheets with parchment and spray with cooking spray. Pipe potatoes onto the sheet in 3-inch circles, about 2-inches in height, leaving about 2-inches between mounds (the potatoes will spread slightly as they bake). Freeze for 15 minutes, until just firm.
Gently brush potato mounds with melted butter and sprinkle with remaining Parmigiano Reggiano.
Bake until tops are golden and centers are hot, about 20 minutes. Let stand a few minutes before transferring to a platter with a thin spatula. Serve hot.
Pipe potatoes onto the lined, greased baking sheets, cover loosely with plastic wrap, and refrigerate up to one day in advance of baking (omit the freezing step). 15 minutes before you're ready to bake, uncover and remove baking sheets from refrigerator and proceed with the recipe as directed, brushing the potatoes with butter and sprinkling with Parmesan.