Preheat the oven to 400 degrees F. Coat a 2-quart baking dish with 1 tablespoon butter.

Bring the cream, 1/2 teaspoon salt and the sage to a simmer in a large saucepan over medium-low heat; cook 10 minutes. Meanwhile, peel the potatoes and slice 1/8 inch thick (use a mandoline, if you have one).

Cover the bottom of the prepared dish with about one-quarter of the potatoes, overlapping the slices. Season with salt and cayenne pepper and sprinkle with one-third of the cheese. Repeat the layers 2 more times (potatoes, salt, cayenne, cheese), ending with a layer of potatoes.

Strain the cream, discarding the sage. Pour the cream into the dish and press the potatoes down. Cut the remaining 2 tablespoons butter into pieces and dot over the potatoes. Cover with aluminum foil and transfer to the oven; reduce the oven temperature to 350 degrees F and bake 40 minutes, then uncover and bake until golden and bubbly, about 20 more minutes.

Photograph by Christina Holmes