Prepare the Cheese Sauce

1. Preheat the Oven: Preheat your oven to 350°F (175°C). Grease a 9×13-inch baking dish.
2. Make the Roux: In a medium saucepan, melt butter over medium heat. Add the minced garlic and cook for 1 minute. Stir in the flour and cook for 1-2 minutes until golden and bubbly.
3. Add Milk and Cream: Slowly whisk in the milk and heavy cream. Cook while stirring until the mixture thickens, about 3-5 minutes.
4. Add Cheese: Remove from heat and stir in 2 cups of cheddar cheese and all the Parmesan cheese until melted. Season with salt, black pepper, and paprika.

Assemble and Bake

1. Layer the Potatoes: Arrange half of the sliced potatoes in an overlapping layer in the prepared baking dish.
2. Add Sauce: Pour half of the cheese sauce over the potatoes and spread evenly.
3. Repeat Layers: Add the remaining potatoes and top with the rest of the cheese sauce.
4. Top with Cheese: Sprinkle the remaining 1 cup of cheddar cheese on top.
5. Bake: Cover with foil and bake for 45 minutes. Remove the foil and bake for an additional 25-30 minutes until the potatoes are tender and the top is golden and bubbly.

Finish and Serve

1. Cool Slightly: Let the dish rest for 10 minutes before serving to allow the sauce to thicken.
2. Garnish: Sprinkle with fresh thyme or parsley for a touch of color and flavor.