Step 1

Arrange a rack in the upper third of the oven and heat the oven to 350ºF. Coat a 9x13-inch baking dish with butter.

Step 2

Prepare the following, adding each to a large pot or Dutch oven (preferably wide) as you complete it: Peel 3 pounds russet potatoes, then cut with a chef’s knife or on a mandoline into thin (1/8-inch) thick slices. Finely chop 2 garlic cloves. Pick the leaves from 3 fresh thyme sprigs until you have 1/2 teaspoon, or measure out 1/4 teaspoon dried thyme.

Step 3

Add 3 1/2 cups half-and-half and 2 1/2 teaspoons kosher salt. Bring to a simmer over medium heat, gently folding the potatoes into the sauce every few minutes to bring the potatoes at the bottom to the top, about 13 minutes. Meanwhile, grate 4 ounces Gruyère or white sharp cheddar cheese on the large holes of a box grater (about 1 cup).

Step 4

Turn off the heat. Using the slotted spoon, transfer about half of the potatoes into the baking dish and arrange into an even layer. Sprinkle with half of the cheese. Repeat layering the remaining potatoes, then pour any remaining sauce evenly over the top. Sprinkle with the remaining cheese. Cut 2 tablespoons unsalted butter into 8 pieces and scatter evenly over the top.

Step 5

Bake uncovered until the potatoes in the center are very tender, and the top is dark golden brown, about 1 hour. Garnish with more fresh thyme leaves if desired. Let cool for 10 minutes before serving.