Cook potatoes with 1 teaspoon salt in boiling water to cover 30 to 40 minutes or just until tender. Let cool slightly; peel and slice. Set aside.
Stir together remaining 1/2 teaspoon salt, soup, and next 3 ingredients until blended.
Layer half each of potato slices, barbecue sauce mixture, and cheese in a lightly greased 2-quart round baking dish. Repeat layers; sprinkle top evenly with paprika.
Bake at 350° for 45 minutes or until golden.