Step 1: Prepare the potatoes

1. Preheat your oven to 375°F (190°C). Grease a 9×13-inch (23×33 cm) baking dish with butter or nonstick spray.
2. Peel the potatoes and slice them thinly (about 1/8-inch thick). Use a mandoline slicer for even slices, if available.

Step 2: Make the cheese sauce

1. In a medium saucepan, melt the butter over medium heat. Add the minced garlic and sauté for 1 minute until fragrant.
2. Whisk in the flour and cook for 1-2 minutes, stirring constantly, to create a roux.
3. Gradually add the milk, whisking continuously to prevent lumps. Cook for 3-4 minutes until the mixture begins to thicken.
4. Remove from heat and stir in the cheddar cheese, Parmesan, salt, pepper, and smoked paprika (if using). Mix until the cheese is fully melted and the sauce is smooth.

Step 3: Layer the potatoes and sauce

1. Arrange half of the sliced potatoes in an even layer in the prepared baking dish.
2. Pour half of the cheese sauce over the potatoes, spreading it evenly.
3. Repeat with the remaining potatoes and cheese sauce, ensuring all slices are coated.

Step 4: Add the topping

1. Sprinkle the shredded Gruyère cheese (if using) over the top layer.

Step 5: Bake the au gratin potatoes

1. Cover the dish with aluminum foil and bake for 40 minutes.
2. Remove the foil and bake for an additional 20-25 minutes, or until the potatoes are tender and the top is golden and bubbly.

Step 6: Serve

1. Let the dish rest for 5 minutes before serving. Garnish with chopped fresh parsley, if desired.