Put the potatoes into a large pot, and add enough cold water to cover the potatoes by 2 inches. Bring to a boil over high heat, and then add the 1/2 teaspoon salt. Then then lower the heat, and let the potatoes simmer until fork tender -- about 20 minutes. Drain the potatoes in a colander, and then return them to the pot.
Over low heat, gently stir the potatoes for about 1 minute to allow moisture to evaporate. Then mash the potatoes to a smooth puree. Off heat, stir in the butter. When the butter is well incorporated, stir in the seasonings. Taste carefully -- you might like to add more salt. Let the mixture cool until warm, not hot. Then stir in the egg yolks until they are well incorporated.
If you are planning to bake right away, preheat the oven to 400°F.
Transfer the potato mixture to a large piping bag that is outfitted with a large star tip. Also, line a baking sheet with parchment paper. Pipe the potatoes into decorative swirls or some other shape, roughly 2 inches in diameter.
MAKE AHEAD NOTE: At this point, the Duchess Potatoes can be frozen for weeks or even months. Freeze them directly on the baking sheet. When they are solidly frozen, transfer them to an air-tight container. Arrange the potatoes on a baking sheet when you are ready to bake. Do not thaw the potatoes prior to baking.
Bake in the preheated oven until the swirls turn golden brown -- usually 20-25 minutes. Serve hot or warm.