Step 1

Arrange a rack in the upper third of the oven and second rack below it. Line the lower rack with aluminum foil to catch any drips. Heat the oven to 450ºF. Coat an 18x13-inch rimmed baking sheet (half sheet pan) with unsalted butter. Coat one side of a sheet or two of aluminum foil large enough to cover the baking sheet with butter.

Step 2

Bring 3 1/4 cups half-and-half, 2 minced garlic cloves, 2 1/2 teaspoons kosher salt, and 1/4 teaspoon dried thyme to a simmer over medium heat in a small saucepan, stirring until the salt is dissolved. Turn off the heat.

Step 3

Peel 3 pounds russet potatoes, then cut with a chef’s knife or on a mandoline into thin (1/8-inch-thick) slices. Arrange half of the potatoes on the baking sheet into an even layer (some overlapping is okay). Sprinkle evenly with 4 ounces of the shredded Gruyère cheese.

Step 4

Pour about half of the half-and-half mixture (1 2/3 cups) evenly over the potatoes. Arrange the remaining potatoes evenly over the cheese. Pour the remaining half-and-half mixture evenly over the potatoes (the baking sheet will be very full). Cover the baking sheet tightly with the foil buttered-side down.

Step 5

Bake for 20 minutes. Uncover and sprinkle with the remaining 4 ounces shredded Gruyère cheese and 1 ounce finely grated Parmesan cheese. Return to the oven and bake uncovered until the potatoes in the center are very tender, and the top is well-browned, about 20 minutes more. Sprinkle with 2 tablespoons finely chopped fresh chives if desired. Let cool for 5 minutes before serving.