Preheat your oven to 350F and move the rack to the middle position.
Meanwhile, grate the cheese and prepare the potatoes by peeling them and using a mandoline slicer to cut them into 1/8" (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 and Tony's seasoning. Let it warm through, stirring occasionally, until the seasoning has been fully mixed in. As it reaches a boil, take it off the heat.
Arrange half of the potatoes on the bottom of an 8x8 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 uncovered for 70-75 minutes. Ovens vary, so I would check after 60 minutes if your oven runs hot. A toothpick should slide into the potatoes easily without much resistance.
Let the potatoes sit for 5 minutes prior to serving.