1. Preheat oven to 375°. Grease a large baking dish all over with butter and place on top of a baking sheet (to catch any cream that might overflow). Peel potatoes then cut into very thin slices, about ¼” thick. (Using a mandoline if you have one!) Place in a bowl and cover with water to prevent browning.
2. In a small saucepan over medium heat, combine half-and-half, garlic and thyme. Heat mixture until bubbles begin to form around the edges. Stir in 1 ½ cups Parmesan then season with salt and pepper. Remove from heat.
3. Drain potatoes and pat dry with paper towels or a clean kitchen towel. Arrange potatoes in the baking dish, fanning the potatoes to look like shingles. Pour warm cream mixture over the potatoes and press down on the potatoes to make sure that every potato is coated. Sprinkle with remaining Parmesan.
4. Bake until the top is bubbling and golden and the potatoes are tender, about 1 hour 15 minutes.
5. Serve warm.

https://www.delish.com/cooking/recipe-ideas/recipes/a57231/garlic-parm-au-gratin-recipe/