Bring a large pot of salted water to the boil. Cook potatoes in the boiling water until they are just becoming tender, approximately 8 to 10 minutes. Refrigerate the potatoes overnight.
Preheat oven to 180 C / Gas 4.
Grate the potatoes. In a small bowl, combine 1 teaspoon parsley, 1 teaspoon salt, 1/4 teaspoon pepper, 1 tablespoon finely chopped onion and half of the butter. In a separate small bowl, combine soured cream and milk.
Layer half of the grated potatoes into the bottom of the prepared baking dish. Sprinkle the dried spice mixture over the layer of potatoes. Pour half of the soured cream and milk mixture over the potatoes and butter layers. Top this layer with half of processed cheese. Repeat the layering process one more time.