Preheat your oven to 400°F (200°C). Butter a 9x13 inch baking dish or similar.

Peel the potatoes and slice them thinly, using a mandoline slicer for uniform thickness if possible.

In a large saucepan, combine the heavy cream, whole milk, minced garlic, salt, pepper, and nutmeg. Bring the mixture to a simmer over medium heat. Add the sliced potatoes to the saucepan, ensuring they are submerged. Let them simmer gently for about 10 minutes, stirring occasionally, until the potatoes have started to soften.

Using a slotted spoon, transfer half of the potatoes to the prepared baking dish, spreading them out evenly. Sprinkle half of the grated cheese over the potatoes. Repeat with the remaining potatoes and cheese, creating layers.

Pour the remaining cream mixture from the saucepan over the layered potatoes and cheese in the baking dish.

Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes. Then, remove the foil and continue baking for another 20-30 minutes, or until the top is golden brown and the potatoes are tender when pierced with a knife.

Let the Potatoes au Gratin rest for about 10 minutes before serving. This allows the layers to set and makes it easier to serve.