Prep Dish & Slice Potatoes: Preheat oven to 375°F (190°C). Generously grease a 9x13-inch ceramic baking dish with butter. Using a mandoline slicer, slice unpeeled Yukon Gold potatoes into uniform 1/8-inch rounds.

Make Garlic Thyme Cream Sauce: In a medium saucepan, melt 4 tbsp butter over medium heat. Add minced garlic and cook for 1 minute until fragrant. Whisk in flour and cook for 1 to 2 minutes until bubbly. Gradually whisk in heavy cream and whole milk to prevent lumps. Simmer for 3 to 4 minutes until thickened. Stir in fresh thyme, sea salt, black pepper, and freshly grated nutmeg. Remove from heat.

Melt Cheese into Sauce: Whisk 1/2 cup of the shredded Gruyère and 1/2 cup of white cheddar directly into the warm sauce until smooth and melted.

Layer Potatoes: Arrange one-third of the potato slices in overlapping shingled rows across the bottom of the dish. Pour one-third of the warm cream sauce over the potatoes and sprinkle with 1/3 cup of cheese. Repeat with a second layer of potatoes, sauce, and cheese.

Top Layer & Bake Covered: Add the final layer of potatoes, pour the remaining cream sauce over top, and crown with the remaining Gruyère and cheddar. Cover the baking dish tightly with buttered aluminum foil (buttered side down so cheese doesn't stick). Bake at 375°F for 45 minutes until potatoes are knife-tender.

Uncover & Brown: Remove foil and bake uncovered for an additional 20 to 25 minutes, or until the top is deeply golden brown, bubbly, and caramelized. Rest for 15 minutes before serving to allow the rich cream to set!