01 -
Preheat oven to 350°F and position rack in the middle of the oven.
02 -
Grate cheddar and parmesan cheeses. Peel potatoes and slice into 1/8-inch rounds using a mandoline slicer.
03 -
Melt butter in a small saucepan over medium-high heat. Add minced garlic and cook for 30 seconds. Pour in heavy cream, add salt and pepper, and heat until just beginning to boil. Remove from heat once warmed through.
04 -
Arrange half of the sliced potatoes in an overlapping layer on the bottom of a greased 9x13-inch baking dish. Pour half of the cream mixture over the potatoes and sprinkle with half of each cheese. Repeat these layers with remaining potatoes, cream, and cheese, finishing with a cheese layer on top.
05 -
Cover the dish with aluminum foil and bake for 40 minutes. Uncover and continue baking for an additional 25 to 35 minutes, or until potatoes are tender and a toothpick inserted meets little resistance. Monitor for doneness, as oven temperatures may vary.