Preheat the oven to 375°F. Butter a 9×13 inch oven-proof dish and set aside.
Heat the cream, milk, garlic, salt and pepper in a small saucepan over medium heat until simmering. Reduce the heat to low and simmer for about 10 minutes or until the liquid has reduced slightly. Turn off the heat.
Peel the potatoes and place in a bowl of cold water to keep them from discoloring. Using a mandolin or a sharp knife, slice the potatoes thinly (about ⅛-inch). If you do not have a mandolin, use a sharp knife to slice the potatoes as thinly as you can.
Layer a third of the potato slices, slightly overlapping, in the dish, and sprinkle 1/3 of the cheese on top. Repeat until you have three layers of potatoes. Sprinkle the remaining cheese and the rosemary on top. Pour over the cream and milk mixture.
Bake until the cheese is golden brown and the liquid is bubbling around the edges, about 50-60 minutes. If the top isn’t golden brown after 60 minutes, turn the broiler on for a few minutes to color and crisp the cheese. Remove from the oven and cover with foil. Allow to stand for 5-10 minutes before cutting into it to serve.
Switch it up. You can pair quite a few different flavors with potatoes. Try using different kinds of cheese (blue cheese could work well), other root vegetables like celeriac layered in with the potatoes or for something really special, add some black truffle shavings.