Preheat the oven to 350 degrees F. Rub the garlic around the bottom and sides of a 9-inch x 9-inch baking dish. Remove the garlic from the dish and set aside in a bowl.
Using a sharp chef's knife or a mandoline slicer, cut the potatoes into very thin slices. Place in a large bowl and set aside.
Place a large pot over medium-high heat. Whisk together the garlic, butter, half-and-half, salt, pepper, and nutmeg. Bring it to a simmer.
Add the potatoes and bring to a boil. Cook until the sauce begins to thicken, about 5 to 7 minutes.
Transfer the potatoes to your prepared baking dish, and then carefully pour the sauce over the potatoes. (I like putting the potatoes in first so that they don't splash into the hot liquid.) Use a large spoon to distribute the potatoes evenly in the dish.
Bake for 1 hour. Spoon the sauce over the potatoes a couple of times during baking to keep the potatoes on top from drying out.
When cooking time is up, the top will be golden brown and the sauce will be bubbling. Remove from the oven and let rest for 10 to 15 minutes before serving.
Notes
Prep ahead tip: Cut all the potatoes and put them into a large bowl. Cover with water and store them in the refrigerator. Drain the water just before you're ready to cook.