Bake the potatoes in a preheated 400 degree F oven for 1 hour, or until they are tender.
Halve the potatoes lengthwise, scrape the flesh into a bowl, and press them through a ricer into a large bowl. With an electric mixer beat in the butter, 1 tablespoon at a time, the whole eggs, 1 at a time, and the half-and-half and beat the mixture until it is combined well and smooth. Add 1/3 cup of Parmesan. Add the nutmeg, pepper, and salt, to taste, and transfer the mixture to a pastry bag fitted with a large decorative tip.
Pipe the mixture into 6 rosettes onto a buttered baking sheet and drizzle them with the melted butter and remaining cheese. (The rosettes may be chilled, covered loosely, for several hours or overnight). Bake the potatoes in a preheated 350 degree F oven for 10 to 15 minutes for potatoes at room temperature, or for 25 to 30 minutes for chilled potatoes, or until they are heated through. Then, put the baking sheet under a preheated broiler about 6 inches from the heat, and broil the potatoes until the tops are golden.