Preheat the oven to 400 degrees F. Butter an 8 by 8-inch casserole dish using 1 tablespoon of the butter.
In a pot, add the heavy cream, 1/2 teaspoon salt, and sage leaves. Bring to a simmer and steep for 10 minutes. While steeping, peel and slice the potatoes 1/8-inch thick on a mandolin. Begin to layer the potatoes on the bottom of the prepared dish, overlapping each slice by half. When the first layer of potatoes is complete, season with salt, cayenne pepper, and sprinkle with a third of the cheese. Repeat two more times, ending with a final layer of just potatoes.
Strain the heavy cream and discard the sage. Pour the heavy cream over the casserole, pressing the potatoes down. Dot the remaining 2 tablespoons butter in pieces evenly over the top of the potatoes. Cover with aluminum foil and place in the oven, lowering the temperature to 350 degrees F. Bake, covered, for 40 minutes. Uncover and bake 20 minutes more. Serve hot.