1. Preheat the oven to 425 F.
2. Lightly grease a shallow 1 1/2 quart casserole dish with butter.
3. Peel potatoes, and then slice, using a mandolin.
4. Now grate Gruyère or Emmenthaler cheese.
5. Next arrange the sliced potatoes and layer with melted butter.Season with salt and pepper and sprinkle with the cheese.
6. Layer with melted butter and half and half. Season with salt and pepper.
7. Top with more grated cheese and sprinkle with Parmesan.
8. Bake the casserole covered for 30 minutes
9. After 30 minutes, uncover and bake an additional 15 minutes or until the potatoes are tender.