Preheat the oven to 375°.
Butter a 3-quart baking dish.
Sprinkle the minced garlic over the bottom of the baking dish.
Arrange a single layer of potato slices in the baking dish; season with salt and pepper and sprinkle evenly with a few tablespoons of the shredded Cheddar cheese. Repeat layers until all of the potatoes are used.
In a bowl, whisk the egg, milk, and cream until smooth. Pour over the potatoes and sprinkle any remaining cheese over the top. Bake until the potatoes are tender and the casserole is bubbly and golden brown, about 55 to 65 minutes.
Calories per serving: 315
Fat per serving: 19.2