Preheat your oven to 375°F (190°C). Grease a 2-quart casserole dish with butter or oil.
Peel the potatoes and slice them thinly into even rounds, about 1/8 inch thick. Core and thinly slice the cabbage.
In a small bowl or measuring cup, combine the heavy cream, kosher salt, and black pepper.
Arrange a single layer of overlapping potato slices across the bottom of the prepared casserole dish. Cover with a layer of sliced cabbage.
Drizzle a little of the seasoned cream over the vegetables.
Continue layering potatoes and cabbage with cream until all the vegetables have been used, finishing with a layer of potatoes.
Pour any remaining cream evenly over the top and sprinkle with the shredded cheese.
Cover the casserole dish with foil and bake for 40 minutes.
Remove the foil and continue baking for 20–30 minutes, until the top is golden brown and the vegetables are tender.
Let the gratin cool for about 10 minutes before serving.
