Preheat the oven to 350 degrees F and butter a baking dish with a fews tablespoons of softened butter.

Arrange a layer of potatoes in the baking dish, and sprinkle some of the cheeses over them. Continue layering potatoes and cheeses until you've used them all, ending with a layer of potatoes. Seat aside a small handful of cheeses for the top.

In a small saucepan, heat cream over a low flame. Whisk the cream with the salt and pepper, paprika, and a little of the butter. Pour this over the potatoes, making sure to pour into the corners of the baking dish as well. Sprinkle remaining cheese on top of potatoes.

Bake, uncovered for about 45 minutes or until the potatoes are tender and golden brown on top. Let stand for 5 minutes before serving.