Preheat the oven to 400 degrees F. Coat the bottom and sides of an 8-by-8-inch baking dish with the butter; set aside.
In a saucepot on medium heat, add the heavy cream, sage, garlic and a pinch of salt. Bring to a low simmer and cook until the cream becomes fragrant with the scent of sage, about 10 minutes.
Layer the potatoes in the prepared dish. Add each slice by overlapping the previous slice by a bit and continue this pattern in a row or create a spiral. Once the first layer is done, sprinkle with a pinch of salt and cayenne pepper. Repeat the next layers by doing the same. Once the layers are complete, strain out the sage leaves and garlic from the heavy cream and pour the cream over the dish. Allow the cream to settle into the dish, picking it up a little bit off the counter, then dropping it to tap the air out. Then, sprinkle with the cheese. Cover the dish with aluminum foil.
Lower the oven temperature to 350 degrees F. Bake the potatoes for 45 minutes; remove the cover and bake until the cheese is golden, about 15 more minutes.