Step 1

Arrange a rack in the middle of the oven and heat the oven to 350°F. Rub 2 tablespoons unsalted butter on the bottom and sides of a 10-inch cast-iron or ovenproof high-sided skillet.

Step 2

Peel 4 pounds medium Yukon Gold potatoes. Use a mandoline or a sharp knife to thinly slice 1/8- to 1/4-inch thick.

Step 3

Prepare the following, adding each to the same large bowl as you complete it: Grate 4 ounces Gruyère or sharp white cheddar cheese on the large holes of a box grater (about 1 cup). Finely grate 4 ounces Parmesan cheese on a Microplane or the smallest holes of a box grater (about 1 cup). Mince or grate 5 garlic cloves (about 1 tablespoon.) Pick the leaves from 1 bunch fresh thyme and finely chop until you have 4 teaspoons.

Step 4

Add 2 1/4 cups heavy cream, 1 teaspoon kosher salt, 1 teaspoon black pepper, and 1/4 teaspoon ground nutmeg to the bowl and stir to combine. Transfer half of the mixture to the skillet and spread into an even layer.

Step 5

Arrange the potato slices in a spiral shape in the skillet, working your way from the outside towards the center: Stack a handful of larger similar-sized slices together, then place the stack vertically in the skillet so that you can see the edges of all the slices, nestling them into the cream mixture slightly. Continue stacking and arranging, using the larger slices first and then working your way down in size so the smaller ones are in the center.

Step 6

Spoon the remaining cream mixture evenly over the potatoes. The cream should come about 1/2 inch to the top of the skillet. If you have too much, don’t use it all. Place the skillet on a rimmed baking sheet.

Step 7

Bake until the top is deep golden brown and the potatoes are tender, 1 hour 40 minutes to 1 hour 50 minutes. (You can remove one slice of potato from the center of the skillet and check for doneness if you’re unsure.) Check after 1 hour and 15 minutes: If the top is already browned, loosely cover the top with aluminum foil and continue baking. Let cool for 10 minutes before serving. Garnish with more fresh thyme leaves if desired.