Bring a large pot of salted water to boil, place potatoes in the boiling water. Let potatoes cook until they are just becoming tender, approximately 8 to 10 minutes. Refrigerate the potatoes overnight.
Preheat oven to 350 degrees F (175 degrees C).
Grate the potatoes. In a small bowl, combine 1 teaspoon parsley, 1 teaspoon salt, 1/4 teaspoon pepper, 1 tablespoon minced onion, and 1/2 of the butter or margarine. In a separate small bowl, combine sour cream and milk.
Layer 1/2 of the grated potatoes into the bottom of the prepared baking dish. Sprinkle the dried spice mixture over the layer of potatoes. Pour 1/2 of the sour cream and milk mixture over the potatoes and butter layers. Top this layer with 1/2 cup of processed cheese spread. Repeat the layering process one more time.
