Preheat oven to 375°F (190°C) and grease a baking dish.
In a saucepan, melt butter over medium heat, then add minced garlic and cook until fragrant.
Stir in heavy cream, milk, salt, pepper, and paprika. Simmer for 2 minutes.
Layer half of the sliced potatoes in the baking dish and pour half of the cream mixture over them.
Sprinkle half of the cheddar cheese on top.
Repeat the layering process with the remaining potatoes, cream mixture, and cheese.
Sprinkle grated Parmesan cheese on top.
Cover with foil and bake for 30 minutes. Remove foil and bake for another 15 minutes until golden and bubbly.
Let it cool for 5 minutes before serving.