Set a rack in your oven at middle position and preheat to 400°F.
In a large bowl, combine the cheeses. Set aside about 1/3 of the combined cheeses for later in a separate smaller bowl.
To the rest of the cheeses in the big bowl, add the cream, salt, garlic, smoked paprika, and black pepper. Mix thoroughly, let stand while you prep potatoes.
Wash and peel the potatoes.
CAREFULLY using a mandolin (or really great knife skills), slice potatoes by the ends at 1/8" thickness.
Stir the cream and cheese mixture a bit to ensure evenly mixed. Add potatoes to the mixture, folding to cover and coat. Let stand 15 minutes.
Evenly coat the inside of your casserole dish with the butter. Pick up a handful of potatoes, organizing them into a neat stack, and lay them in the casserole dish with their edges aligned vertically. Continue placing potatoes in the dish, working around the perimeter and into the center until all the potatoes have been added. The potatoes should be very tightly packed. If necessary, slice an additional potato, coat with cream mixture, and add to casserole. Pour the excess cream/cheese mixture evenly over the potatoes until the mixture comes halfway up the sides of the casserole. You may not need all the excess liquid.
Cover dish tightly with foil and transfer to the oven. Bake for 30 minutes. Remove foil and continue baking until the top is pale golden brown, about 30 minutes longer. Carefully remove from oven, sprinkle with remaining cheese, and return to oven. Bake until deep golden brown and crisp on top, about 30 minutes longer. Remove from oven, let rest for a 20-30 minutes, and serve.