Preheat the oven to 400 degrees.
Bake the potatoes in the oven for 1 hour, or until tender. Halve them lengthwise and scrape the pulp into a bowl. Press pulp through a ricer into a large bowl. Reduce the heat to 350 degrees. With an electric mixer beat in the softened butter, 1 tablespoon at a time, the eggs and yolks, 1 at a time, and the half-and-half. Beat until smooth and add the nutmeg, salt and white pepper. Transfer the mixture to a pastry bag fitted with a large decorative tip. On a buttered baking sheet pipe into 14 large rosettes and drizzle them with the melted butter. The rosettes can be made 1 day ahead and kept refrigerated, covered loosely. Bake the rosettes in the middle of the oven for 10 to 15 minutes if the potatoes are at room temperature or for 25 to 30 minutes if chilled, or until heated through. Put them under the broiler about 6 inches from the heat until the tops are golden. Serve on platter with the ballotine.