Preparation

• Position a rack in the center of the oven and heat the oven to 350°F. Line a rimmed baking sheet with foil. Grease a 9×13-inch baking dish with the butter.
• Pour the milk and cream into a small saucepan. Add the garlic, rosemary, and nutmeg. Bring just to a simmer, cover, and remove from the heat. Set aside to infuse for at least 20 minutes. Combine the Swiss cheese and Parmigiano in a bowl.
• Peel the potatoes and, using a mandoline or your sharpest knife, slice them into 1/8-inch-thick rounds. Arrange about one-third of the potatoes in a single overlapping layer in the baking dish, season with kosher salt and white pepper, and top with one-third of the Swiss-Parmigiano mix. Scatter over half of the goat cheese. Add a second overlapping layer of potatoes, more salt and white pepper, another third of the Swiss- Parmigiano mix, and the remaining goat cheese. Make a third layer with the remaining potatoes and season with salt and white pepper. Press down lightly to compact the layer
• Remove the garlic and rosemary from the infused cream, and discard them. Set the cream over medium-high heat and watch carefully until it just begins to simmer; don’t let it boil. Pour the cream over the potatoes and sprinkle the remaining cheese on top.
• Set the baking dish on the foillined baking sheet, and bake until the top is deeply brown and the potatoes are completely tender when poked with a skewer, 1-1/4 to 1-1/2 hours. Let sit for 10 to 15 minutes before serving.