Preheat the oven to 375 degrees F. Grease a 9-by-13-inch baking dish with butter, and set aside.
Sprinkle a layer of crushed soda crackers on the bottom of the prepared baking dish. Arrange a layer of oysters, along with their juices, on top of the crackers. Sprinkle with salt and pepper and dot with a few pats of butter. Repeat, beginning with another layer of crackers. Top with a final layer of soda crackers and then pour the cream over everything. Sprinkle with the Parmesan and paprika. Bake until golden brown and bubbly, 45 minutes to 1 hour.