Place the peeled and cubed potatoes in a large pot and cover them with cold water. Add a pinch of salt and bring the water to a boil. Reduce the heat and simmer for about 15 minutes, or until the potatoes are very tender when pierced with a fork. Drain the potatoes thoroughly in a colander.
Return the drained potatoes to the warm pot for a minute to let any excess moisture evaporate. Use a potato masher or a ricer to mash the potatoes until they are completely smooth and free of lumps. It is important to do this while they are hot to ensure a creamy consistency.
Add the softened butter, heavy cream, salt, black pepper, and nutmeg to the mashed potatoes. Stir everything together until the butter is fully melted and the mixture is well combined. Taste and adjust the seasoning if necessary.
Allow the potato mixture to cool slightly for a few minutes so you do not scramble the eggs. Stir in the three egg yolks until the mixture is uniform and holds its shape. The egg yolks are essential as they provide the structure and help the potatoes brown beautifully in the oven.
Preheat your oven to 400 degrees Fahrenheit and line a baking sheet with parchment paper. Transfer the potato mixture into a large piping bag fitted with a large star tip. Pipe the potatoes into 3 inch wide swirls on the prepared baking sheet, leaving space between each one.
Place the baking sheet in the oven and bake for 15 to 20 minutes. You want the edges and peaks of the swirls to turn a lovely golden brown. Once finished, remove them from the oven and let them rest for a couple of minutes before serving.
