Preheat your oven to 350F and move the rack to the middle position.

Meanwhile, grate the cheeses and prepare the potatoes by peeling them and using a mandoline slicer to cut them into ⅛" (3 mm) slices.

Add the butter to a small saucepan over medium-high heat, and once it's melted, add the garlic and cook it for about 30 seconds. Add in the cream, salt, and some pepper. Let it warm through, stirring occasionally. As it reaches a boil, take it off the heat.

Arrange half of the potatoes on the bottom of a greased 9x13 baking dish (overlap the potatoes but don't worry about arranging them perfectly). Pour half the cream mixture over top, and then add half of each cheese. Repeat the process for the second layer, finishing up with a layer of cheese on top.

Bake, covered with foil, for 40 minutes, then remove the foil and bake for another 25-35 minutes or until a toothpick slides into the potatoes without much resistance.

Let the potatoes sit for 5-10 minutes prior to serving.