Prepare the Cream Mixture:
In a medium saucepan, combine the heavy cream, milk, minced garlic, salt, black pepper, and ground nutmeg.
Heat over medium heat until the mixture begins to simmer. Remove from heat and set aside.
Assemble the Gratin:
Arrange a layer of sliced potatoes in the bottom of the prepared baking dish, slightly overlapping each slice.
Pour about 1/3 of the cream mixture over the potatoes, then sprinkle with 1/3 of the shredded cheese.
Repeat the layers twice more, ending with the remaining cheese on top. Dot the top layer with the small pieces of butter.
Bake the Gratin:
Cover the baking dish with aluminum foil and bake in the preheated oven for 45 minutes.
Remove the foil and continue baking for an additional 30-35 minutes, or until the top is golden brown and the potatoes are tender when pierced with a fork.
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