Preheat the oven to 350 degrees F.
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.
Recipe courtesy of B. Smith, B. Smith's Entertaining and Cooking For Friends, Artisan, 1995