Preheat oven to 170 °C. Generously oil a large deep rectangular baking dish.
Peel the potatoes and cut them with a mandolin grater or with a knife in very thin (2-3 mm) circles.
Mix the warmed milk and melted cheese, pepper. Add the garlic passed through the press.
Lay out the potatoes slightly overlapping layers, each layer a little prisalivaya and pour the cheese-milk mixture. When all the potatoes lay out, fill it with the remaining mixture. Oil the foil on one side and close the mold. Place in the center of the oven and bake for 30 minutes.
Remove the foil, put thin slices of butter on the potatoes (about 50 g) and return to the oven for another 10-15 min., the potatoes should be browned. Serve the gratin hot.