Peel and wash the potatoes and cut them into thin slices. Quarter apples, peel and cut out the core. Cut apples into thin slices. Peel sausage skins and cut the sausage into thin slices. Grease a gratin dish and layer the potato, apple and sausage slices. Mix cream and milk.
Peel garlic and put it through a garlic press. Wash the thyme, dab dry and chop finely. Add to the milk-cream together with the garlic and season with salt and pepper. Pour over the gratin and bake in a preheated oven (electric range: 175 °C/ gas: level 2) for 45-50 minutes. Grate the cheese and sprinkle it over the gratin about 20 minutes before the end of the cooking time. Garnish with thyme and serve