Preheat the oven to 400 degrees F. Lightly grease a 2-quart square baking dish with the butter.
Bring the cream to a simmer in a large saucepan over medium-high heat. Add the salt and pepper and stir well. Add the potatoes, adding more cream as necessary to completely cover them. Lower the heat to medium-low and simmer until the potatoes are barely fork tender, 10 to 12 minutes. Remove from the heat.
With a large spoon, transfer 1/3 of the potatoes (both Idaho and sweet), with some of the cream, to the prepared dish, making an even layer. Top with 1/3 of the cheese, and continue layering the potatoes and cheese, ending with cheese, and topping each layer with some of the cream remaining in the pan. Make sure to add enough cream to each layer so that the potatoes are just covered with cream. (You probably will not use all of the cream remaining in the saucepan. Discard any remaining cream.)
Place the dish on a baking sheet and roast until golden brown and bubbly, about 30 minutes. Remove from the oven and let sit for 5 minutes.