1. Preheat the oven to 375° F.

2. Butter the bottom and sides of a 13 × 9 × 2-inch gratin dish. Then, scatter the minced garlic over the bottom.

3. Make a single layer of potato slices in the dish, season with salt and pepper, and sprinkle with a few tablespoons of cheese. Repeat the layers until all the potatoes are used.

4. Whisk together the egg, milk, and cream; pour this mixture over the potatoes. Sprinkle all the remaining cheese on top.

5. Bake until the potatoes are tender and the top is bubbling and golden brown, about 1 hour. Serve piping hot.