Toss sliced potatoes in 1/2 teaspoon cream of tartar and 1 cup water. Drain. Put half of ham, potatoes, and onions in crockpot. Sprinkle with salt and pepper, then grated cheese. Repeat with remaining half. Spoon undiluted soup over top. Sprinkle with paprika.
Cover and cook on Low 8 to 10 hours or High for 4 hours.