Preheat Oven:
Preheat your oven to 375°F (190°C). Grease a 9x13-inch baking dish with butter or nonstick spray.
Prepare the Potatoes:
Peel and thinly slice the potatoes into about 1/8-inch thick rounds. You can use a mandoline slicer for uniform slices or a sharp knife.
Make the Sauce:
In a medium saucepan, melt the butter over medium heat. Once melted, add the flour and whisk continuously to form a smooth roux. Cook for about 1 minute, then slowly pour in the cream and milk while whisking to avoid lumps. Stir in the garlic powder, onion powder, salt, and pepper. Continue to cook, stirring constantly, until the sauce thickens (about 3-4 minutes).
Assemble the Dish:
Layer half of the sliced potatoes in the prepared baking dish. Pour half of the creamy sauce over the potatoes, followed by half of the shredded cheddar cheese and a sprinkle of Parmesan. Repeat with the remaining potatoes, sauce, and cheese.
Bake:
Cover the baking dish with aluminum foil and bake in the preheated oven for 40 minutes. After 40 minutes, remove the foil and bake for an additional 20-25 minutes, or until the top is golden brown and bubbly, and the potatoes are fork-tender.
Serve:
Let the potatoes au gratin rest for 5-10 minutes before serving. Garnish with fresh parsley if desired.