In a large bowl, whisk half-and-half, milk, goat cheese, garlic, flour, salt, pepper and nutmeg. Arrange potato slices in a single layer in a medium greased baking dish. Pour 1/4 of the milk mixture over top, then layer potato slices and add another 1/4 of the milk mixture. Repeat with remaining potato slices and milk mixture until you reach the top of the dish.
Bake for 1 hour and 10 minutes, or until potato gratin is tender and bubbly.