Step 1

Heat the oven to 350°F.

Step 2

Melt 2 tablespoons unsalted butter in a 10-inch cast iron or ovenproof high-sided skillet over medium heat. Add 1 thinly sliced medium yellow onion, 4 fresh thyme sprigs, 1 1/2 teaspoons kosher salt, and 1 teaspoon black pepper. Stir to combine, cover, and cook undisturbed for 5 minutes. Uncover, stir, cover again, and cook for 5 minutes more.

Step 3

Uncover and continue to cook, stirring occasionally at first and then more frequently once the onions start to brown, until the onions are a rich caramel brown color, 8 to 15 minutes more.

Step 4

Sprinkle 1 teaspoon all-purpose flour over the onions, stir well, and cook for about 1 minute to lightly toast the flour. Stir in 1/4 cup dry white wine and cook, scraping the bottom of the skillet, until absorbed, about 1 minute.

Step 5

Remove the skillet from the heat. Stir in 1 1/2 cups low-sodium beef broth. Remove and discard the thyme stems.

Step 6

Arrange 2 1/2 pounds peeled and sliced Yukon Gold potatoes vertically in the skillet: Stack about 10 slices at a time, then lay the stack on its side in the skillet and push down on it a little for a slight shingling effect.

Step 7

Stir 2 ounces of the shredded Gruyère cheese and 2 ounces of the grated Parmesan cheese together in a small bowl. While using one hand to riffle through the potato slices (like flipping through pages in a filing cabinet), sprinkle the cheese mixture with the other hand so a little gets in between each slice. (Don’t worry about getting it in every crevice.)

Step 8

Place the skillet on a rimmed baking sheet. Transfer to the oven and bake for 30 minutes. Meanwhile, place the remaining 2 ounces Gruyère and 2 ounces Parmesan in the now-empty cheese bowl. Stir in 1/2 cup heavy cream.

Step 9

Spoon the cream and cheese mixture evenly over the potatoes. Return to the oven and bake until the top is deep golden-brown with dark brown splotches, and the potatoes are tender, about 30 minutes more.

Step 10

Let cool for 20 minutes. Garnish with fresh thyme leaves before serving.