Put oven rack in middle position and preheat oven to 350°F.
Peel potatoes and cut into 1/8-inch-thick slices with a knife or an adjustable-blade slicer, spreading slices out on a large kitchen towel. Sprinkle with sea salt (1 1/2 teaspoons).
Stir together cream and milk.
Dot bottom of a 3-quart shallow baking dish (13 by 9 inches) with half of butter and pour in 1/3 cup cream mixture. Without rinsing or drying potatoes, divide into 5 piles. Layer potatoes in baking dish, 1 pile per layer, spreading 1/3 cup cream mixture and one fourth of cheese between layers. Drizzle remaining cream mixture over potatoes and dot with remaining butter.
Bake, uncovered, until potatoes are very tender and top is browned, about 2 hours. Let stand at room temperature 10 minutes before serving.