Preheat oven to 375°F (190°C). Grease a baking dish with butter or non-stick spray.
In a saucepan over medium heat, melt butter and sauté garlic until fragrant.
Add heavy cream, milk, salt, black pepper, and paprika. Stir and heat until warm.
Layer half of the sliced potatoes in the baking dish. Pour half of the cream mixture over them.
Sprinkle half of the shredded cheddar cheese over the potatoes.
Repeat the layers with the remaining potatoes, cream mixture, and cheese.
Top with grated Parmesan cheese and cover with foil.
Bake for 40 minutes covered, then remove foil and bake for another 20 minutes until golden brown.
Garnish with fresh parsley before serving.