Butter a 1 1/2 quart baking dish with about 1 tablespoon of the 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.

In a small bowl, whisk the cream with the salt and pepper; pour this over the potatoes. Dot the remaining butter over the top and sprinkle with the paprika. Bake for 1 to 1 1/4 hours, or until the potatoes are tender and golden brown on top. Let stand for 5 minutes before serving.