Parboil potatoes for 15 minutes until barely tender. Drain, peel them and cut into thick slices. Preheat oven to 350 degrees.
With some of the melted butter, lightly grease bottom of shallow casserole. Arrange all of the potato slices overlapping in the bottom of a casserole and season well with salt and pepper; sprinkle with half of Parmesan.
Arrange tomatoes over potatoes and season them with salt and pepper and half of parsley. Scatter mozzarella over tomatoes. Mix parsley with melted butter and season with salt and pepper and scatter over mozzarella. Top with remaining Parmesan and bake for 25 minutes or until all ingredients are hot and cheese is melted.