Wash the peeled potatoes and cut them into round slices, sprinkle with salt and pepper and half the grated cheese. Stir well and pour into a buttered oven dish to which you've added the crushed garlic.
Pour a mixture of the beaten egg with the milk over the potatoes and sprinkle on the remaining cheese. Arrange pieces of butter on top.
Put the gratin to bake in a 392°F (200 °C) oven for about 40-45 min. Once the potatoes soften and redden, the gratin is ready.