Preheat the oven to 350°F. Lightly rub the inside of an 8-by-8-inch casserole dish with the smashed garlic, then allow it to dry. Rub the inside of the dish with butter as well.

Place the sliced potatoes, remaining garlic, remaining butter, half-and-half, salt, pepper, and nutmeg in a medium saucepan.

Set the pan over medium-high heat and bring the mixture to a gentle boil. Cook for about 5 minutes, stirring often, until the liquid begins to thicken.

Pour the potato mixture into the prepared baking dish and gently shake the dish to distribute the slices evenly.

Bake for about 1 hour, occasionally spooning the creamy mixture over the top, until the potatoes are golden and bubbling.

Let the dish cool for 10 minutes before serving so the layers can set.