Preheat the oven to 400°F with a rack in the center position. Grease a 9x13-inch baking dish with 1 tablespoon of the butter.
Add the heavy cream, garlic, nutmeg, and remaining 3 tablespoons butter to a small sauce pan and set it over low heat. Cook, stirring, until warmed though. Remove from the heat.
Meanwhile, fill a large bowl with cold water. Peel the potatoes. Using a mandoline, cut the potatoes into ⅛-inch-thick slices and add to the cold water.
Drain the potatoes and pat them completely dry with paper towels.
Arrange ¼ of the potatoes on the bottom of the prepared baking dish, season with ¼ teaspoon of the salt and ⅛ teaspoon of the pepper, then sprinkle with ⅓ cup Gruyère cheese. Repeat 3 more times, ending with the remaining ½ cup Gruyère on top.
Slowly pour the warm cream mixture over the potatoes, then gently press down with a spatula to make sure the liquid is evenly distributed. Sprinkle all over with the Parmesan cheese.
Cover the dish with foil and bake for 50 minutes, then remove the foil and continue to bake until bubbling and lightly browned, about 25 more minutes.